Multiple choice

A coin is biased so that the head is $3$ times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

  1. $P(T=0)=\dfrac{11}{16}$
  2. $P(T=1)=\dfrac{6}{16}$
  3. $P(T=2)=\dfrac{13}{16}$

  4. none of these
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B Correct answer
Explanation

P(H) = 3/4, P(T) = 1/4. Tossing twice: outcomes are HH, HT, TH, TT. P(T=0) = P(HH) = 9/16. P(T=1) = P(HT) + P(TH) = 3/16 + 3/16 = 6/16. P(T=2) = P(TT) = 1/16.

AI explanation

Given that a head is three times as likely as a tail, the probability of a tail is 1/4 and the probability of a head is 3/4. When the coin is tossed twice, the probability of obtaining exactly one tail is found using the binomial distribution: 2C1 times (1/4) times (3/4). This calculation results in 6/16.

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