Multiple choice

$A$ tosses $2$ coins while $B$ tosses $3$. The probability that $B$ obtains more numbers of head is

  1. $\dfrac{1}{4}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{3}{4}$
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C Correct answer
Explanation

A tosses 2 coins (outcomes: 0, 1, 2 heads) and B tosses 3 coins (outcomes: 0, 1, 2, 3 heads). By calculating the probability distribution for both, the probability that B has more heads than A is exactly 1/2.

AI explanation

B must obtain more heads than A to win, where A flips 2 coins and B flips 3 coins, meaning B needs 1, 2, or 3 heads. The probabilities of A obtaining 0, 1, or 2 heads are 1/4, 1/2, and 1/4, respectively. If A gets 0 heads, B wins with a probability of 7/8; if A gets 1 head, B wins with a probability of 1/2; and if A gets 2 heads, B wins with a probability of 1/8. Using the law of total probability, B's overall probability of winning is (1/4 * 7/8) + (1/2 * 1/2) + (1/4 * 1/8), which sums to 1/2.

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