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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 57
Total: 101
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.
Solution:  
Let X denote the random variable which represents the number of tails on the biased coin tossed twice.
∴ X can assume values 0, 1, 2
let p be the probability of tail appears =
1
4

q be the probability of head appears =
3
4

∴ P(X = 0) = Probability that both heads appears =q×q=
3
4
×
3
4
=
9
16

P(X = 1) = Probability that one head & one tail appears =2(p×q) =2(
1
4
×
3
4
)=
3
8

and P(X = 2) = Probability that both tails appears =p×p=
1
4
×
1
4
=
1
16
 X  0  1  2
  P(X)  
9
16
  
3
8
  
1
16
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