Question

A math teacher gave her class two tests. 65% of the class passed the first test given that they also passed the second test. The percentages that the class passed the first test and second test are 70% and 50% respectively.

i) What is the probability for those who passed both tests?

ii) What is the probability for those who passed the second test given that they passed the first test?

iii) What is the probability for those who passed first test or second test?

Answer 1

Given

The percentages that the class passed the first test = 70%

P(passed first test) = 0.70

The percentages that the class passed the second test = 50%

P(passed second test) = 0.50

P( passed first test / passed second test ) = 0.65

When two events, A and B, are dependent, the probability of both occurring is:

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

i)

The probability for those who passed both tests

= P( passed both tests)

= P(passes second test) . P( passed first test / passed second test)

= 0.50 * 0.65

= 0.325

The probability for those who passed both tests is 0.325

ii)

P(passed second test / passed first test)

= P( passed both tests ) / P( passed first test)

= 0.325 / 0.70

0.4643

The probability for those who passed the second test given that they passed the first test is 0.4643

iii)

The probability for those who passed first test or second test

= P(passed first test) + P( passed second test ) - P( passed both tests)

= 0.70 + 0.50 - 0.325

= 0.875

The probability for those who passed first test or second test is 0.875