Question

A coin is flipped three times; give the probability distribution of the number of heads.

Answer 1

Given that, A coin is flipped three times.

Let, X: random variable denoting that number of heads.

i.e X takes the value 0, 1, 2, 3

Now if a coin is flipped three times then the sample space is given by, [ Let, H=Head , T=Tail ]

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

From the sample space we get,

Number of total outcomes = 8

3 times Head = 1 ; {HHH}

2 times Head = 3 ;  {HHT, HTH, THH}

1 times Head = 3 ; {HTT, THT, TTH}

0 times Head = 1 ; {TTT}

i.e. Prob(Three heads)=1/8 , Prob(Two heads)=3/8 , Prob(one head)=3/8 , Prob(Zero head)=1/8

[ Since probability of a certain event A is given by, P(A)= (number of favorable outcomes to the event A/number of total outcomes) ]

Answer:-

So, the probability distribution of the number of heads is give by,

x:	0	1	2	3	Total
P(X=x)	1/8	3/8	3/8	1/8	1