Multiple choice

A biased coin has the probability of the appearance of a head twice as likely as that of a tail. If the coin is tossed three times, what are the chances of getting exactly two heads?

  1. 66.66%

  2. 55.55%

  3. 48%

  4. 44.44%
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D Correct answer
Explanation

P(H) = 2/3, P(T) = 1/3. For 3 tosses, exactly 2 heads: 3 * (2/3)^2 * (1/3) = 3 * (4/9) * (1/3) = 12/27 = 4/9 = 44.44%.

AI explanation

Since the probability of getting a head is twice that of a tail, the probability of a head is 2/3 and the probability of a tail is 1/3. Using the binomial probability formula for exactly k successes in n trials, the probability of exactly two heads in three tosses is 3C2 times (2/3) squared times (1/3) to the power of one. This calculates to 3 times 4/9 times 1/3, which equals 12/27. Simplifying this fraction gives 4/9, which is 44.44 percent.

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