Question

If two coins are tossed, find the probability of the following events.
A) Getting at least one head.
B) Getting no head.

Answer 1

Sample space = HH,HT,TT,THHH,HT,TT,TH

Lets us define these two events:

A: Heads on both coins.

B: Atleast one head(one or more)

Since its a case of conditional probability.

We know

P(A|B)=P(A∩B)P(B)P(A|B)=P(A∩B)P(B)

Lets us calculate numerator

P(A∩B)=P(A)P(A∩B)=P(A)(Think of it as like thisP(X=2|X>1)=P(X=2)P(X=2|X>1)=P(X=2))

P(A)P(A)=P(P(Heads on both coins)=$\frac{1}{4}$

P(B)P(B)=P(P(Atleast one head)=$\frac{3}{4}$

P(A|B)=$\frac{\frac{1}{4}}{\frac{3}{4}}$P(A|B)=$\frac{\frac{1}{4}}{\frac{3}{4}}$

P(A|B)=$\frac{1}{3}$