Question

x is a binomial random variable with n=10 and p=.5. find the probability of obtaining from 6 to 9 tails of a fair coin. use the binomial probability distribution formula

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.5

N = number of trials = 10

R = desired success = 6 to 9

P(6) + P(7) + P(8) + P(9)

= 10c6*(0.5^6)*(1-0.6)^10-6 + 10c7*(0.5^7)*(0.5)^10-7 + 10c8*(0.5^8)*(0.5)^10-8 + 10c9*(0.5^9)*(0.5)^10-9

= 0.3759765625