Proability

[hariharakarthi]

A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

[gmat_dest]

Probability of blue card = 2/8

Probability of not blue card = 6/8

Probability of both cards being not blue = 6/8 * 5/7 = 15/28

[tom4lax]

Wouldn't the easiest way to approach this problem be to determine the probability that both are blue?

1st card blue = 2/8
2nd card blue = 1/7

2/8 * 1/7 = 1/28 both are blue

1 - 1/28 = 27/28 neither are blue

Whats the OA?

[ankitns]

If the probability of both being blue is 1/28.

1 - 1/28 = 27/28 will give us the probability that BOTH OF THEM ARE NOT BLUE at the same time. This means that you could have 1 blue and 1 other color...or 2 other colors. So this approach will not work.

Wouldn't the easiest way to approach this problem be to determine the probability that both are blue?

1st card blue = 2/8
2nd card blue = 1/7

2/8 * 1/7 = 1/28 both are blue

1 - 1/28 = 27/28 neither are blue

Whats the OA?

[umaa]

Probability of both are blue = 2/8 * 1/7 = 1/28

So, the probability of both are not blue is, 1-(1/28) = 27/28

[mohitsharda]

Wouldn't the easiest way to approach this problem be to determine the probability that both are blue?

1st card blue = 2/8
2nd card blue = 1/7

2/8 * 1/7 = 1/28 both are blue

1 - 1/28 = 27/28 neither are blue

Whats the OA?

I think that the case that you are taking is that both are blue. and then subtracting it to get the case when both are not blue. But the question should be interpreted as not even a single card is blue. In this reasoning you are taking cases when 1 is blue and other is not and hence you are getting 27/28

gmat_dest is right in the way he has solved it.. according to me

[ankitns]

Could you please clarify the last sentence "what is the probability that they will both are not blue?"

Do you mean that they are BOTH not blue

or

Do you mean that NEITHER of them are blue (which means that at most 1 of them can be blue).

Depending on that, the question changes and hence the probability changes.

Thanks.

quote="hariharakarthi"]A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?[/quote]

[tom4lax]

Okay, got it guys, thanks.

Question is asking probability that NEITHER is blue.

2/8 first card is blue, so 6/8 it isnt

5/7 second card is not blue

5/7 * 6/8 = 15/28