Multiple choice

Each of two persons tosses three fair coins. The probability that they obtain the same number of heads, is

  1. 1/2

  2. 5/16

  3. 7/16

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Each person tosses 3 coins. The probability distribution for heads is: 0 heads (1/8), 1 head (3/8), 2 heads (3/8), 3 heads (1/8). The probability they get the same number of heads is the sum of the squares of these probabilities: (1/8)^2 + (3/8)^2 + (3/8)^2 + (1/8)^2 = (1 + 9 + 9 + 1) / 64 = 20 / 64 = 5/16.

AI explanation

Using the binomial distribution, the probability of getting k heads for each person is found by combining the probabilities that both obtain exactly k heads. The probabilities for obtaining zero, one, two, and three heads are 1/8, 3/8, 3/8, and 1/8, respectively. We square each probability and sum the results: (1/8)^2 + (3/8)^2 + (3/8)^2 + (1/8)^2 = 1/64 + 9/64 + 9/64 + 1/64 = 20/64 = 5/16. The probability they obtain the same number of heads is 5/16.

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