# Find the probability that a person fails the first time but passes the second?

The probability that a person passes organic chemistry the first time he enrolls is .8 The probability that a person passes organic chemistry the second time he enrolls is .9 .

a) Find the probability that a person fails the first time but passes the second time.

B. Find the probability that a person fails both times.

(a)

The probability of the person passes the organic chemistry first time is .

The probability of the person passes the organic chemistry second time is .

The probability of the person fails first time is .

The probability of the person fails second time is .

The probability that a person fails the first time but passes the second time is .

The events and are independent events : .

Substitute and .

.

The probability that a person fails the first time but passes the second time is .

(b)

From part (a):

The probability of the person fails first time is .

The probability of the person fails second time is .

The probability that a person fails both times is .

The events and are independent events : .

.

The probability that a person fails both times is .