Bunuel wrote:
A box contains exactly 24 balls, of which 12 are red and 12 are blue. If two balls are to be picked from this box at random and without replacement, what is the probability that both balls will be red?
(A) 11/46
(B) 1/4
(C) 5/12
(D) 17/40
(E) 19/40
Straightforward:
\(\frac{favorable.outcome}{possible.outcomes}\) for 2 picks, then multiply.
Pick #1: 12 red balls. 24 balls total
Probability of red in 1st pick: \(\frac{12}{24}=\frac{1}{2}\)
Now there are 11 red and 23 total balls. (There's no replacement.)
Probability of red in 2nd pick: \(\frac{11}{23}\)
Multiply probability of both picks.
P(2 successive reds):
\((\frac{1}{2}*\frac{11}{23}) =\frac{11}{46}\)
Answer A
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