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Homework answers / question archive / Question 1 of 5 A blood test is 99% effective in detecting a certain disease when the disease is present
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Question 1 of 5 A blood test is 99% effective in detecting a certain disease when the disease is present. However, the test also yields a false-positive result for 2% of the healthy patients tested. Suppose 0.5% of the population has the disease. Find the conditional probability that a randomly tested individual actually has the disease given that his or her test result is positive. Select the nearest number.
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If P(A) = 0.3, P(B) = 0.4, and P(A|B) = 0.5, then P(A or B) is
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When the weather is clear, the sharpshooter can hit the target with probability 0.9; when it is foggy, the probability drops to 0.6. According to weather forecast, at the time of competition tomorrow the weather will be clear with probability 0.8, and will be foggy with probability 0.2. What is the probability that the sharpshooter will hit the target at the competition tomorrow?
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Which of the following pair of events would be the best example of two independent events?
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Each time a basketball player attempts a free throw, he will make it with probability 0.8. Suppose the player attempts 2 free throws, what is the probability that he will make exactly 1 of them?
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Since E1? and E2? are events complimentary to each other.
∴P(E1?)+P(E2?)=1
⇒P(E2?)=1−P(E1?)=1−0.005=0.995
Let A be the event that the blood test result is positive.
P(E1?)=0.5% ?=0.005
P(A?E1?)=P(result is positive given the person has disease)=99% =0.99
P(A?E2?)=P(result is positive given that the person has no disease)=2% =0.02
Probability that a person has a disease, given that his test result is positive, is given by P(E1??A).
By using Baye's theorem, we obtain
P(E1??A)=P(E1?)⋅P(A?E1?)/(P(E2?)⋅(A?E2?)+P(E1?)⋅P(A?E1?)?)
0.199
Ans 2:
First compute
P(A and B) = P(A|B) P(B) = 0.5 x 0.4 =0.2.
Therefore,
P(A or B) = P(A) + P(B) - P(A and B) = 0.3 + 0.4 - 0.2 = 0.5
It is also helpful to fill out the joint probability table.
Ans 3: 0.9*0.8+0.6*0.2 = 0.84
Ans 4: C
Ans 5: 0.32
