If a certain coin is flipped, the probability that the coin will land heads up is 1/2...

Question

If a certain coin is flipped, the probability that the coin will land heads up is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

GMAT Panda · Accepted Answer

1/32 We first translate "the probability that the coin will land heads up is 1/2", giving the probability of heads and tails. P(H) = 1/2 P(T) = 1 - 1/2 = 1/2 We then multiply the probabilities of independent flips to find the probability that the coin lands heads on the first three flips and tails on the last two flips. P(H then H then H then T then T) = P(H)^3 P(T)^2 = (1/2)^3 (1/2)^2 = (1/2)^5 = 1/32

Explanation	Calculations	Help
$We first translate "the probability that the coin will land heads up is 1/2", giving the probability of heads and tails.$	$P (H) = \frac{1}{2} P (T) = 1 - \frac{1}{2} = \frac{1}{2}$
$We then multiply the probabilities of independent flips to find the probability that the coin lands heads on the first three flips and tails on the last two flips.$	$P (H then H then H then T then T) = P (H)^{3} \times P (T)^{2} = (\frac{1}{2})^{3} \times (\frac{1}{2})^{2} = (\frac{1}{2})^{5} = \frac{1}{32}$

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