Multiple choice

Three unbiased coins are tossed. What is the probability of getting (i) exactly two heads (ii) at least two heads (iii) at most two heads?

  1. 3 8 , 6 8 , 1 4

  2. 3 8 , 1 2 , 7 8

  3. 3 8 , 1 2 , 1 8

  4. 5 6 , 1 3 , 1 4

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes = 2^3 = 8. (i) Exactly two heads: {HHT, HTH, THH} = 3/8. (ii) At least two heads: {HHT, HTH, THH, HHH} = 4/8 = 1/2. (iii) At most two heads: 1 - P(HHH) = 1 - 1/8 = 7/8.

AI explanation

Using the classical definition of probability, the total possible outcomes when tossing three coins is 2 times 2 times 2 = 8. The probability of exactly two heads is 3/8 since the favorable outcomes are three. The probability of at least two heads includes outcomes with two or three heads, equalling (3 + 1)/8 = 1/2. The probability of at most two heads includes outcomes with zero, one, or two heads, equalling (1 + 3 + 3)/8 = 7/8.

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