Question

One of the problems encountered with organ transplants is the body's rejection of the transplanted tissue. If the antigens attached to the tissue cells of the donor and receiver match, the body will accept the transplanted tissue. Although the antigens in identical twins always match, the probability of a match in other siblings is .25. If you have 7 siblings and all of them offer a kidney, what is the probability that at least two will match?

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 = 0.25

N = number of trials = 7

R = desired success = at least 2

We know that sum of all the probabilities is = 1

So, p(at least 2) = 1 - (p(0) + p(1))

= 0.55505371093