Question

Five individuals have responded to a request by a blood bank for blood donations. None of them has donated before, so their blood types are unknown. Suppose only type O is desired and only one of the five actually has this type. If the potential donors are selected in random order for typing, what is the probability that at least four individuals must be typed to obtain the desired type

Answer 1

Answer:

The probability that at least four individuals must be typed to obtain the desired type is P=0.2.

Step-by-step explanation:

The donors are randomly selected to be typed.

The probability of selecting a random donor and it does not have type O is 4/5=0.8.

The probability of selecting the second donor and he does not have type O is 3/4, as one of the donors has been already tested and does not have type O.

Then, we can apply the same reasoning for the next two donors and calculate the probability that at least four individuals as:

$P(k=4)=\left(\dfrac{4}{5}\right)\cdot\left(\dfrac{3}{4}\right)\cdot\left(\dfrac{2}{3}\right)\cdot\left(\dfrac{1}{2}\right)=\dfrac{1}{5}=0.2$