Question

Two bolts are drawn from a box containing 4 good and 6 bad bolts. Find the probability that the second bolt is good, if the first one is found to be bad.

Answer 1

Answer:

Two bolts are drawn from a box containing 4 good and 6 bad bolts. the probability that the second bolt is good, if the first one is found to be bad is 4/10

Step-by-step explanation:

This is a question of conditional probability.

Now, given two possible outcomes A and B:

P(A/B) = The probability of A given B.

It is given by:

P(A/B) = P(A ∩ B)/ P(B)

Now let the probability that of getting a bad bolt be = 6/10 (B)

That of getting a good bolt = 4/10 (A)

The probability that the second bolt is good given that the first one is bad is given by:

P(A/B) = (4/10 × 6/10) / (6/10)

= 24/100 ÷ 6/10 = 4/10