A coin is biased so that the head is 3 times as likely to occur as tail. if the coin is tossed 3 times. what is the probability of getting a tail??
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Let X denotes the random variable which denotes the number of tails when a biased coin is tossed twice.
So, X may have value 0, 1 or 2.
Since, the coin is biased in which head is 3 times as likely to occur as a tail.
∴ P{H} = 3/4 and P{T} = 1/4
P(X = 1) = P{HH} = (3/4)^2 = 9/16
P(X = 1) = P (one tail and one head) = P{HT,TH} = P{HT} + P{TH} + P{H}P{T} + P {T} P{H}
= 3/4 x 1/4 + 1/4 x 3/4
= 3/16 + 3/16
= 6/16
= 3/8
P (X = 2) = P (two tails) = P{TT} = P{T} P{T} = (1/4)2 = 1/16
Therefore, the required probability distribution is as follows :
(This is a table⬇️)
x | P(X)
0 | 9/16
1 | 3/8
2. | 1/16
So, X may have value 0, 1 or 2.
Since, the coin is biased in which head is 3 times as likely to occur as a tail.
∴ P{H} = 3/4 and P{T} = 1/4
P(X = 1) = P{HH} = (3/4)^2 = 9/16
P(X = 1) = P (one tail and one head) = P{HT,TH} = P{HT} + P{TH} + P{H}P{T} + P {T} P{H}
= 3/4 x 1/4 + 1/4 x 3/4
= 3/16 + 3/16
= 6/16
= 3/8
P (X = 2) = P (two tails) = P{TT} = P{T} P{T} = (1/4)2 = 1/16
Therefore, the required probability distribution is as follows :
(This is a table⬇️)
x | P(X)
0 | 9/16
1 | 3/8
2. | 1/16
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