Question

A math teacher gave her class two tests. 40% of the class passed both tests and 80% of the class passed the first test. What percent of those who passed the first test also passed the second test (given the following formula for conditional probability)? Round your answer to the nearest whole percentage point.

P(B|A) = P(A and B) / P(A)

Select one:

a. 50%

b. 20%

c. 60%

d. 40%

q-2

Assume that you had a constraint satisfaction problem where you had the following set of numbers {1,2,3,4,5,6 } and you had to discover which numbers from the set could be added together to result in the sum of 7, which of the following would represent a breath first approach to building the search graph for solving this problem?

Select one:

a.

b.

c.

Q -3-----You go to see the doctor. The doctor selects you at random to have a blood test for swine flu, which for the purposes of this exercise we will say is currently suspected to affect 1 in 10,000. The test is 96% accurate, in the sense that the probability of a false positive is 4%. The probability of a false negative is zero. You test positive. What is the new probability that you have swine flu? (round to the nearest thousands place … 3 decimal places)

Answer 1

(1) 40% of the class passed both the tests. So, P(Both) = 0.4

80% of the class passed the first. So, P(First) = 0.8

We can use conditional probability here.

P(Second | First) = P(Both) / P(First) = 0.4 / 0.8 = 0.5

So, 50% of the class  who passed the first test also passed the second test.

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(2) There are no options given in this question.

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(3) We can use Bayes' Theorem here.

FIrst of all, let P(S) be the probability that you have swine flu.

Let P(~S) be the probability that you don't have swine flu.

Let P(T) be the probability of a positive test.

We have to find P(S | T). (The probability that you have swine flu if the test is positive).

According to Bayes' theorem,

P(S | T) = P(T | S) * P(S) / (P(T | S) * P(S) + P(T | ~S) * P(~S))

We are given, P(S) = 0.0001 (1 in 10000 people)

P(~S) = 0.9999 (Probability of not having swine flu)

P(T|S) = 1 (If you have swine flu, test will be positive since there's no false negatives)

P(T|~S) = 0.04 (There is a 4% chance of a false positive)

So, P(S|T) = 1 * 0.0001 / (1 * 0.0001 + 0.04 * 0.9999) = 0.0025

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Let me know if you have any doubts in the comments. Please upvote if the answer helped you.