11 Plus Exams Forum

is two fair dice are thrown, then what is the probability of getting an even number on one and an odd number in the other? this is from 'Book name: elevenplusexams book 2 numerical reasoning (It has 10 tests)' .


page number 41 question 4d - test 7:

this answer according to me should be 18/36 = 1/2 so answer at the back of the book seems wrong as it says 1/4.

according to me the successful choices are like {(2,1) {2,3), (3,2),(1,2),...}

please can someone advise me as I am not quite confused. thanks a lot for your help in advance

I would have thought it was 1/2 too, with 1/4 chance of both odd and 1/4 chance of both even.

Hi

The probablity of getting an even number of one dice = 1/2. Probability of getting odd number on the other dice = 1/2

Prob of getting even on one and odd on another = 1/2X1/2 = 1/4

I know the question is a bit misleading as the answer assumes that one of the dice only provides even scores and the other only provides odd scores.

It is wrong - you need to consider both ways round.

It doesn't matter what the first die gives just that the second one is the opposite ...

I think it's useful to view this as being analogous to an outcome of head and tail when two coins are tossed. The probability is the 1/2 because the possible outcomes are:
HT TH HH TT

nyr

gulat summarises it well.

Alternatively, if you do a table of outcomes you will find that there are 6 x 6 = 36 total outcomes with the two dice. Only 9 give you the (even, odd) outcome. So the answer is 9/36 or 1/4.

36 outcomes indeed but 18 fit the odd plus even:

1,2: 1,4: 1,6

2,1: 2,3: 2,5

3,2: 3,4: 3,6

4,1: 4,3: 4,5

5,2: 5,4: 5,6

6,1: 6,3: 6,5

Sometimes one needs to understand the answer on the basis that that the question is not that well worded. The book's answer is for the outcomes where the first die gives an even. That is how I understood the question on first reading it.

Then the question is wrong as probability always considers both options unless told specifically that the order is important.

JB - I do teach maths!

thanks for your help and advise, everyone. i m now convinced that correct answer of this question is 1/2. i am a master of science in maths and i was pretty sure question/answer combination is wrong. there is at least one more probability question in the same book elsewhere that is wrong. i will write to them.