Question

One-third of blood donors at a clinic have O+blood.(a) Assuming that there is a very large number of donors at the clinic and the donors are independent of each other, find the probability that

(i) six or more donors have to be screened in order to find two who have O+blood.

(ii) among six donors screened, more than two do not have O+blood.

(iii) more than six donors have to be screened in order to find the first with O+blood.

(iv) Find the expected number of donors who must be screened in order to find five with O+blood.

Answer 1

i)

P(X=   2   )=   1C1*0.3333^2*0.667^0=       0.1111
P(X=   3   )=   2C1*0.3333^2*0.667^1=       0.1481
P(X=   4   )=   3C1*0.3333^2*0.667^2=       0.1481  
P(X=   5   )=   4C1*0.3333^2*0.667^3=       0.1317
P(6 or more) = 1 - 0.1111 - 0.1481- 0.1481 - 0.1317 = 0.5390

ii) P(X>2) = 0.3196

iii)

P(x>6) = 0.0879

iv)

mean=µ = r/p= 5/(1/3) = 15