Hello, badi6!

Here's #6 . . .

We are given: .

Bayes' Theorem: .

Substitute: .

Therefore: .

b) Draw a Venn diagram to represent these data. Code:

* - - - - - - - - - - - - - - - - - - - *
| |
| * - - - - - - - * |
| | H | |
| | * - - - + - - - * |
| | 5/24 | | | |
| | | 5/12 | | |
| | | | 1/12 | |
| * - - - + - - - * | |
| | W | |
| * - - - - - - - * |
| 7/24 |
* - - - - - - - - - - - - - - - - - - - *

Find the probability that:

c) only one of them has passed their driving test.

d) neither of them has passed their driving test.

Two couples are chosen at random.

e) Find the proability that only one of the two husbands and

only one of the two wives have passed their driving test. One husband passed and the other failed.

This can happen in two ways:

. .

Hence: .

One wife passed and the other failed.

This can happen in two ways:

. .

Hence: .

Therefore: .