Question

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

Answer 1

(i) When one coin is tossed twice, the sample space is

{HH, HT, TH, TT}

Let X represent the number of heads.

∴ X (HH) = 2, X (HT) = 1, X (TH) = 1, X (TT) = 0

Therefore, X can take the value of 0, 1, or 2.

It is known that,

P (X = 0) = P (TT)

P (X = 1) = P (HT) + P (TH)

P (X = 2) = P (HH)

Thus, the required probability distribution is as follows.

X	0	1	2
P (X)

(ii) When three coins are tossed simultaneously, the sample space is

Let X represent the number of tails.

It can be seen that X can take the value of 0, 1, 2, or 3.

P (X = 0) = P (HHH) =

P (X = 1) = P (HHT) + P (HTH) + P (THH) =

P (X = 2) = P (HTT) + P (THT) + P (TTH) =

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

Thus, the probability distribution is as follows.

X	0	1	2	3
P (X)

(iii) When a coin is tossed four times, the sample space is

Let X be the random variable, which represents the number of heads.

It can be seen that X can take the value of 0, 1, 2, 3, or 4.

P (X = 0) = P (TTTT) =

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

=

P (X = 2) = P (HHTT) + P (THHT) + P (TTHH) + P (HTTH) + P (HTHT)

+ P (THTH)

=

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

=

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

Thus, the probability distribution is as follows.

X	0	1	2	3	4
P (X)