Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Probability

For married couples the probability that the husband has passed his driving test is 7/10 and the probability that the wife has passed her driving test is 1/2. The probability that the husband has passed, given that the wife has passed, is 14/15.

i) Find the probability that, for a randomly chosen married couple, the driving test will have been passed by:

a) both of them - 7/15
b) only one of them - 4/15
c) neither of them - 4/15

ii) If two married couples are chosen at random, find the probability that only one of the husbands and only one of the wives will have passed the driving test.

It is this last one that I am having trouble with. I have shown my answers (which match the back of the book) for the other ones to make it easier for anyone who wants to help . I manage to get to the correct answer for part ii) - 119/450, but only by writing out all the different combinations and calculating their individual probabilities. I am convinced there is a much easier and quicker way, but I am too tired to try to think of one. This is a question from a past exam, so I doubt they would expect a candidate to write out all the combinations.

Can anyone help?

Thanks

Last edited by Daniel123 (2008-02-16 10:36:31)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Probability

Has no one got any ideas?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Probability

Let

From 1(a)

Then

And from 1(c)

So the answer to the second part is

Was this what you did?

Last edited by JaneFairfax (2008-02-17 08:15:39)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Probability

Well yes and no.. this is basically what I did, but I didn't do it as concisely as you. In fact, looking back my way is rather stupid.

Thank you Jane.