Let W be a random variable giving the number of tails minus the number of heads in three tosses of a coin. Assuming that a tail is three times as likely to occur, find the probability distribution of the random variable W.

Explanation:

In a toss of a coin; the are two possibilities of events happening;

Either a Head or a Tail.

Given data:

Let W be a random variable giving the number of tails minus the number of heads in three tosses of a coin.

So; W = [ HHH, HHT, HTH, HTT, TTT, THT, TTH , THH]

Probability distribution of the random variable W for  a tail occurring at three coin will be

W = 3: P(3T)

= P (TTT)

=

=

W = 2 : P(2T, 1H)

= P( HTT, TTH, THT)

= ×

=

=

W = 1 : P(1T, 2H)

= P ( HHT, HTH, THH)

= ×

=

=

W = 0 : P (3H)

= P (HHH)  

=

=

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