The probability that a bearing fails during the first month

The probability that a bearing fails during the first month of use is .18. What is the probability that it does not fail during the first month? An item is manufactured by a certain process that has probability 0.10 of being defective. True or False If a sample of 100 items is drawn, exactly 10 of them will be defective True False An item is manufactured by a certain process that has probability 0.10 of being defective. True or False If a sample of 100 items is drawn, the number of defectives is likely to be close to 10, but not exactly equal to 10. True False Let V be the event that a computer has a virus, and let W be the event that a computer contains a worm. Suppose P(V) = .15, P(W) = .05, and P(V W) = .17. Find the probability that the computer contains both a virus and a worm. Let V be the event that a computer has a virus, and let W be the event that a computer contains a worm. Suppose P(V) = .15, P(W) = .05, and P(V W) = .17. Find the probability that the computer contains a virus but not a worm.

Solution

1) Probability that a bearing does not fail during the first month

= 1 -  Probability that a bearing fail during the first month

= 1 - 0.18

= 0.82

2) Probablity of defective = 0.10 = 10 %

Hence, exactly 10 out of 100 are defective.

Therefore, given statement is TRUE.

3)

Probablity of defective = 0.10 = 10 %

Hence, exactly 10 out of 100 are defective.

Therefore, given statement is FALSE.

4) P(V) = 0.15

P(W) = 0.05

P ( V W) = 0.17

P (V W) = ?

We know that

P (VW) = P(V) + P(W) - P (V W)

= 0.15 + 0.05 - 0.17

= 0.03

Hence, P (VW) = 0.03

Therefore,

Probability that the computer contains both virus and worm = 0.03