Question

Imagine you have an unbalanced coin, which weights more on one side, which causes that the probability of having a head on this coin is 60%. Suppose you toss this coin twice.

(a) What is the probability of having exactly one head?

(b) What is the probability of two heads?

Answer 1

We are given a baised coin hence we have the followng

Probability of head = 0.6
Probability of tail = 0.40

When we toss two coins we have four outcomes.

HEADS HEADS
HEADS TAILS
TAILS HEADS
TAILS TAILS

(a) What is the probability of having exactly one head?
For this we have two outcomes.

HEADS TAILS = 0.6 * 0.4 = 0.24
TAILS HEADS = 0.4 * 0.6 = 0.24

Hence the P(exactly one head) = 0.24 + 0.24 = 0.48

(b) What is the probability of two heads?
For this we have two outcomes.

HEADS HEADS = 0.6 * 0.6 = 0.36

P(two heads) = 0.36