A fair coin is tossed 5 times. Find

Answered question

2022-04-16

A fair coin is tossed 5 times. Find the probability that an even number of heads is tossed or no heads at all are tossed.

Answer & Explanation

nick1337

nick1337

Expert2022-08-03Added 777 answers

A fair coin is tossed 5 times

p(head)=12=p(say) 

Let x be a random variable denoting number of heas hat appear tossing the coin 5 times

X~Bionomial(n=5, p=12)

The probability mass function of x is given by p(x=x)=(nx)px(1-p)n-x;x=0(1)5

=(5x)(0.5)x(1-0.5)5-x

=5x)(0.5)x(0.5)5-x

=  (5x)(0.5)5; x=0(1)5

Now we have to find out the probability of obtaining even number of heads or no heads at all

It appears when x = 2, 4, 0

 Required probability

= p (x = 2, 4, 0)

= p(x=0) + p(x=2) +1(x=4)

(50)(0.5)5+(52)(0.5)5+(54)(0.5)5

(5!0! 5!)(0.5)5+(5!2! 3!)(0.5)5+(5!4! 1!)(0.5)5

=(0.5)5+10 (0.5)5+5 (0.5)5

16 (0.5)5=1632= 12=0.5

 

 

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