Multiple choice

A fair coin is tossed five times. If the out comes are $2$ heads and $3$ tails (in some order), then what is the probability that the fourth toss is a head?

  1. $\displaystyle \frac{1}{4}$
  2. $\displaystyle \frac{2}{5}$
  3. $\displaystyle \frac{1}{2}$
  4. $\displaystyle \frac{3}{5}$
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B Correct answer
AI explanation

The problem asks for the probability that the fourth toss is a head given there are exactly 2 heads in 5 tosses, so we use conditional probability. The sample space consists of the arrangements of 2 heads and 3 tails, giving 5! / (2! * 3!) = 10 equally likely possible sequences. If the fourth toss is fixed as a head, we have 1 head left to place in the remaining 4 positions, which can be done in 4 ways. The required probability is the ratio of favorable outcomes to total outcomes in the reduced sample space, 4/10 = 2/5.

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