Question

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. Select the correct answer from above options

Answer 1

If `P(H)` and `P(T)` are probablity of occurance of head and tail respectively, then, We are given, `P(H) = 3P(T)` Also,`P(H)+P(T) = 1` `4P(T) = 1=>P(T) = 1/4` `P(H) = 3P(T) = 3/4` If coin is tossed twice and both outcomes are head,`P(X=0) = 3/4**3/4 = 9/16` If coin is tossed twice and first outcome is tail and second is head`= 1/4**3/4 = 3/16` If coin is tossed twice and first outcome is head and second is tail` = 3/4**1/4 = 3/16` `P(X=1) = 3/16+3/16 = 3/8` If coin is tossed twice and both outcomes are head,`P(X=2) = 1/4**1/4 = 1/16`