Multiple choice

A and B toss 3 coins each. The probability that they both obtain the same number of heads is

  1. 1 9

  2. 3 16

  3. 5 16

  4. 3 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting k heads in 3 tosses is C(3,k)/8. The probability they both get the same number of heads is the sum of probabilities for k=0, 1, 2, 3: (1/8*1/8) + (3/8*3/8) + (3/8*3/8) + (1/8*1/8) = (1+9+9+1)/64 = 20/64 = 5/16.

AI explanation

When tossing 3 coins, the probabilities of getting 0, 1, 2, or 3 heads are 1/8, 3/8, 3/8 and 1/8 respectively. The probability that both A and B obtain the exact 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. Calculating this gives 1/64 + 9/64 + 9/64 + 1/64, which equals 20/64 or 5/16.

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