GMAT Practice Question: If a certain coin is flipped, the probability that the coin will land heads up is \frac{1}{2}...
Question
If a certain coin is flipped, the probability that the coin will land heads up is \frac{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?
- \frac{3}{5}
- \frac{1}{2}
- \frac{1}{5}
- \frac{1}{8}
- \frac{1}{32}
Topics: probability
Solution
Step 1
We first translate \textbf{"the probability that the coin will land heads up is 1/2"}, giving the probability of heads and tails.
P(\text{H}) = \frac{1}{2} P(\text{T}) = 1 - \frac{1}{2} = \frac{1}{2}
Step 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(\text{H then H then H then T then T}) = P(\text{H})^3 \times P(\text{T})^2 = (\frac{1}{2})^3 \times (\frac{1}{2})^2 = (\frac{1}{2})^5 = \frac{1}{32}
Answer
\frac{1}{32}
