Probability question and solution

Q1. A fair coin is tossed five times.The outcome of each toss is either a head or tail.The probability of getting at least one head is 

Solution.

n=5

r>=1

P=1/2

q=1/2

Binomial distribution formula is used because event is repeated.

=P(x:n,p) = nCx px (1-p)n-x

=P(x:n,p) = 5C0(1/2)^0 (1-p)^5-0

=1-1/32=31/32

Q2.  A fair coin is tossed 10 times .what is the probability that only first two tosses yield head.

Solution:

First two head are fixed so (1/2)^2

Last 8 are tail. So (1/2)^8

Probability that only first two tosses yield head is

=(1/2)^2*(1/2)^8

=(1/2)^10

Q3.If two fair coins flipped and at least one of the outcomes is known to be head what is the probability that both outcomes are heads.

Solution

S={TT,TH,HT,HH}

One of the outcome is known to be a head

{TH,HT,HH}

=Probability that both outcomes are heads

=1/3

Q4. Two coins are tossing together find the probability of getting atleast one head.

Solution:

Sample space={HH,HT,TH,TT}

Atleast one head={HH,HT,TH}

Probability of getting atleast one head=3/4

Q5.Two coins are tossing together find the probability of getting exactly two head.

Solution:

Sample space={HH,HT,TH,TT}

Atleast one head={HH}

Probability of getting atleast one head=1/4