Question

A coin is biased so that it has a 60% chance of landing on heads. If it is thrown three times, find the probability of getting: a) Three heads b) 2 heads and a tail c) At least one head

Answer 1

Answer:

Given a biased coin such that heads is 3 times as likely as tails. The coin is tossed twice.

P(H)=

4

3

and P(T)=

4

1

Let T be the random variable for the number of tails.

P(T=0)=P(HH)=

4

3

×

4

3

=

16

9

P(T=1)=P(HT,TH)=

4

3

×

4

1

+

4

3

×

4

1

=

16

3

+

16

3

=

8

3

=

16

6

P(T=2)=P(TT)=

4

1

×

4

1

=

16

1

Hence (B) is the correct answer.