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A coin is biased so that the probability of tails is 1/3. What is the probability of obtaining exactly two tails on five tosses of the coin ?
This is a binomial distribution with P(success) = 1/3 and n = 5
P(x =2) = 5C 2 (1/3)² (2/3)^3
= 5 x 4/ 2! (1/9) ( 8/27)
= 10 x 8/243
= 0.329 approx to 3 decimal places
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