# Statistics MCQs – Basic probability Part 7

121. An X-ray test is used to detect a disease that occurs, initially without any obvious symptoms, in 3% of the population. The test has the following error rates: 7% of people who are disease free have a positive result and 2% of the people who have the disease have a negative result. A large number of people are screened at random using the test, and those with a positive result are examined further. What proportion of people who have the disease are correctly tested?

a. 0.980

b. 0.302

c. 0.001

d. 0.069

e. 0.542

Answer: A

122. An X-ray test is used to detect a disease that occurs, initially without any obvious symptoms, in 3% of the population. The test has the following error rates: 7% of people who are disease free have a positive result and 2% of the people who have the disease have a negative result. A large number of people are screened at random using the test, and those with a positive result are examined further. What proportion of people with a positive result actually have the disease?

a. 0.980

b. 0.302

c. 0.001

d. 0.069

e. 0.542

Answer: B

123. An X-ray test is used to detect a disease that occurs, initially without any obvious symptoms, in 3% of the population. The test has the following error rates: 7% of people who are disease free have a positive result and 2% of the people who have the disease have a negative result. A large number of people are screened at random using the test, and those with a positive result are examined further. What proportion of people with a negative result actually have the disease?

a. 0.980

b. 0.302

c. 0.001

d. 0.069

e. 0.542

Answer: C

124. An X-ray test is used to detect a disease that occurs, initially without any obvious symptoms, in 3% of the population. The test has the following error rates: 7% of people who are disease free have a positive result and 2% of the people who have the disease have a negative result. A large number of people are screened at random using the test, and those with a positive result are examined further. What proportion of the tests conducted give incorrect results?

a. 0.980

b. 0.302

c. 0.001

d. 0.069

e. 0.542

Answer: D

125. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television. Find the probability that if the wife is watching television, the husband is also watching television.

a. 0.67

b. 0.57

c. 0.53

d. 0.75

e. 0.47

Answer: A

126. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 50% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television. Find the probability that if the wife is watching television, the husband is also watching television.

a. 0.67

b. 0.57

c. 0.53

d. 0.75

e. 0.47

Answer: B

127. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. It has also been determined that when the husband is watching television, 30% of the time the wife is also watching. When the husband is not watching television, 40% of the time the wife is watching television. Find the probability that if the wife is watching television, the husband is also watching television.

a. 0.67

b. 0.57

c. 0.53

d. 0.75

e. 0.47

Answer: C

128. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 20% of the time the wife is watching television. Find the probability that if the wife is watching television, the husband is also watching television.

a. 0.67

b. 0.57

c. 0.53

d. 0.75

e. 0.47

Answer: D

129. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 40% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television. Find the probability that if the wife is watching television, the husband is also watching television.

a. 0.67

b. 0.57

c. 0.53

d. 0.75

e. 0.47

Answer: E

130. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television. Find the probability that the wife is watching television in prime time.

a. 0.36

b. 0.35

c. 0.34

d. 0.32

e. 0.39

Answer: A

131. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 50% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television. Find the probability that the wife is watching television in prime time.

a. 0.36

b. 0.35

c. 0.34

d. 0.32

e. 0.39

Answer: B

132. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. It has also been determined that when the husband is watching television, 30% of the time the wife is also watching. When the husband is not watching television, 40% of the time the wife is watching television. Find the probability that the wife is watching television in prime time.

a. 0.36

b. 0.35

c. 0.34

d. 0.32

e. 0.39

Answer: C

133. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 20% of the time the wife is watching television. Find the probability that the wife is watching television in prime time.

a. 0.36

b. 0.35

c. 0.34

d. 0.32

e. 0.39

Answer: D

134. An advertising executive is studying television-viewing habits of married men and women during prime time hours. On the basis of past viewing records, the executive has determined that during prime time, husbands are watching television 40% of the time. It has also been determined that when the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television. Find the probability that the wife is watching television in prime time.

a. 0.36

b. 0.35

c. 0.34

d. 0.32

e. 0.39

Answer: C

135. According to a recent survey of SA households, the probability that the residents of a household own two cars if their annual household income is over R150,000 is 80%. Of the households surveyed, 60% had incomes over R150,000 and 70% had two cars. What is the probability that the residents of a household own two cars and have an annual household income of over R150,000?

a. 0.48

b. 0.40

c. 0.36

d. 0.52

e. 0.54

Answer: A

136. According to a recent survey of SA households, the probability that the residents of a household own two cars if their annual household income is over R150,000 is 80%. Of the households surveyed, 50% had incomes over R150,000 and 70% had two cars. What is the probability that the residents of a household own two cars and have an annual household income of over R150,000?

a. 0.48

b. 0.40

c. 0.36

d. 0.52

e. 0.54

Answer: B

137. According to a recent survey of SA households, the probability that the residents of a household own two cars if their annual household income is over R150,000 is 60%. Of the households surveyed, 60% had incomes over R150,000 and 70% had two cars. What is the probability that the residents of a household own two cars and have an annual household income of over R150,000?

a. 0.48

b. 0.40

c. 0.36

d. 0.52

e. 0.54

Answer: C

138. According to a recent survey of SA households, the probability that the residents of a household own two cars if their annual household income is over R150,000 is 80%. Of the households surveyed, 65% had incomes over R150,000 and 70% had two cars. What is the probability that the residents of a household own two cars and have an annual household income of over R150,000?

a. 0.48

b. 0.40

c. 0.36

d. 0.52

e. 0.54

Answer: D

139. According to a recent survey of SA households, the probability that the residents of a household own two cars if their annual household income is over R150,000 is 90%. Of the households surveyed, 60% had incomes over R150,000 and 70% had two cars. What is the probability that the residents of a household own two cars and have an annual household income of over R150,000?

a. 0.48

b. 0.40

c. 0.36

d. 0.52

e. 0.54

Answer: E

140. According to a recent survey of SA households, the probability that the residents of a household own two cars if their annual household income is over R150,000 is 80%. Of the households surveyed, 60% had incomes over R150,000 and 70% had two cars. What is the probability that the residents of a household do not own two cars but do have an annual household income of over R150,000?

a. 0.12

b. 0.10

c. 0.24

d. 0.13

e. 0.06

Answer: A