In these questions you have to determine if the statements contain the necessary information to answer the questions.

Each of the 25 balls in a certain bag is either red white or blue, and has a number between 1-10 painted on it. If 1 ball is to be picked a random, what is the probability it will be white or have an even number?

(1) The probability it is white and even = 0
(2) The probability it is white minus the probability it is even = 0.2

A) if statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not;

B) if statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not;

C) if statements (1) and (2) taken together are sufficient to answer the question, even though neither
statement by itself is sufficient;

D) If either statement by itself is sufficient to answer the question;

E) If statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

What do you this the answer is?
I think its (E) but would always love someone to recheck my probability solutions :)

I agree Kamal. All we can deduce given both (1) and (2) is that

P(W U E) = P(W) + P(E) – 0
= 2P(E) + 0.2 (since P(W) – P(E) = 0.2)
or
P(W U E) = 2P(W) – 0.2

and we have no information about P(W) or P(E) so we can’t get to a solution ….

Thanks Mair.

I agree with both of you, but I went about this a slightly different way.
First I thought of the balls as being either white (W) or non-white (W’), even (E) or non-even (E’) and interpreted the conditions in terms of numbers of balls (this was because Mair had already shown that my first instinct (“throw it all into the formula”) wouldn’t work.
In terms of balls, (1) becomes – “there are no white balls that are even”,
and (2) becomes – “There are 5 more white balls than there are even balls” <0.2*25=5>

I thought this might help, but I realised that there was no other relation between white balls or even balls. I tried using equations linking whites, non-whites, evens and non-evens. I hoped that knowing the constraint “there are 25 balls” would help, and to a point it did, but it fell short of giving the solution. I threw my formulae in to a spreadsheet, and got a range of valid solutions to the problem with the number of white balls and even balls ranging between 5-15 and 0-10 respectively. P(WandE) lay between 0.2 and 1.

What I found interesting was that the “number between 1-10” didn’t affect the solution at all, and the number could be any number whatsoever (not confined to integer, rational, or even real – in fact it needn’t be a number at all).

A nice extra condition leading to a unique solution is
(3) – all balls are white or even.

Unfortunately, this does make it a little bit too easy, especially when written in terms of probabilities.

Hey Joe,
Some nice thinking there – great to see another Mathematician here on eduFire.
By the way, I looked at your profile and I think I know you and your family in North East Wales (I am originally from Flint too). What a tiny world it is!