Question

When tossing a fair coin three times what is the probability of getting 0, 1, 2, or 3 heads (as opposed to tails)? Write the answers in fractional notation, corresponding to the order given.

Answer 1

Probability = Favorable Outcomes / Total Outcomes

When tossing a coin n times, the total outcomes = 2³ = 8

When coin is tossed, probability of head = probability of tails = 1/2

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(1) P(0 Heads) = None of the coins should have heads ( all 3 tails) = 3C0 / 8 = 1/8

(Which is the same as saying TTT = 1/2 * 1/2 *1/2 = 1/8)

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(2) P(1 Head) = Out of the 3 tosses, 1 should be heads, and the other 2 tails = 3C1 / 8 = 3/8

(If we do in terms of coins, then the following ways to get 1 head = HTT, THT, TTH, and each will have a probabaility = 1/8. Therefore the required probability = 3/8)

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(3) P(2 Heads) = Out of the 3 tosses, 2 should be heads, and the other 1 tails = 3C2 / 8 = 3/8

(If we do in terms of coins, then the following ways to get 2 heads = HHT, HTH, THH, and each will have a probabaility = 1/8. Therefore the required probability = 3/8)

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(4) P(3 Heads) = Out of the 3 tosses, All 3 should be heads, and no tails = 3C3 / 8 = 1/8

(If we do in terms of coins, then the following ways to get 3 heads = HHH, and the probabaility = 1/8.)

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