Answer:
(a) P(X=1)=0.46
(b) E[X]=1.3
Step-by-step explanation:
(a)
Let A be the event that first coin will land on heads and B be the event that second coin will land on heads.
According to the given information
P(X=1) is the probability of getting exactly one head.
P(X=1) = P(1st heads and 2nd tails ∪ 1st tails and 2nd heads)
= P(1st heads and 2nd tails) + P(1st tails and 2nd heads)
Since the two events are disjoint, therefore we get
Therefore the value of P(X=1) is 0.46.
(b)
Thevalue of E[X] is
..... (1)
First we calculate the value of P(X=2).
P{X = 2} = P(1st heads and 2nd heads)
= P(1st heads)P(2nd heads)
Substitute P(X=1)=0.46 and P(X=2)=0.42 in equation (1).
Therefore the value of E[X] is 1.3.