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  • Find the probability distribution of (iii) number of heads in four tosses of a coin.

Q. 4 Find the probability distribution of 

            (iii) number of heads in four tosses of a coin.

Answers (1)

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When coin is tossed 4 times  then sample space =\left \{ HHHH,HHHT,TTTH,HTHH,THHT,TTHH,HHTT ,TTTT,HTTH,THTH,HTHT,HTTT,THHH,THTT,HHTH,TTHT\right \}

Let X be number of heads.

\therefore  X can be 0,1,2,3,4

 P(X=0)=P(TTTT)=\frac{1}{16}

P(X=1)=P(HTTT)+P(TTTH)+P(THTT)=(TTHT)=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}

P(X=2)=P(THHT)+P(HHTT)+P(HTTH)+P(TTHH)+P(HTHT)+P(THTH)=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{6}{16}=\frac{3}{8}

P(X=3)=P(HHHT)+P(THHH)+P(HHTH)+P(HTHH)=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}

P(X=4)=P(HHHH)=\frac{1}{16}

Table is as shown : 

X 0 1 2 3 4
P(X) \frac{1}{16} \frac{1}{4} \frac{3}{8} \frac{1}{4} \frac{1}{16}

 

Posted by

seema garhwal

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