NCERT Class XII Mathematics Chapter - - Solutions

Question : 53

Total: 101

Find the probability distribution of
(i) number of heads in two tosses of a coin.
(ii) number of tails in the simultaneous tosses of three coins.
(iii) number of heads in four tosses of a coin.

Solution:

(i) The sample space will be = {HH, HT, TH, TT}.
Let X denote the random variable, which represents the number of heads.
∴ X can assumes values 0, 1 and 2.
Hence, the probability distribution is :

P(X)

P(TT)=

P(TH,HT)=

P(HH)=

(ii) The sample space will be = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT }.
Let X denote the random variable, which represents the number of tails.
∴ X can assumes values 0, 1, 2 and 3.
∴ P(X = 0) = P(HHH) =

P(X = 1) = P({HHT, HTH, THH}) =

P(X = 2) = P(TTH, THT, HTT}) =

and P(X = 3) = P(TTT) =

Hence, the probability distribution is :

P(X)

(iii) Here the sample space will be = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT}.
Let X denote random variable, which represents the number of heads.
∴ X can assumes values 0, 1, 2, 3 and 4
∴ P(X = 0) = P(TTTT) =

P(X = 1) = P(HTTT, THTT, TTHT, TTTH) =

P(X = 2) = P(HHTT, HTHT, HTTH, THHT, THTH, TTHH) =

P(X = 3) = P(HHHT, HHTH, HTHH, THHH) =

P(X = 4) = P(HHHH) =

Hence, the probability distribution is :

P(X)

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