the probability of having blood group B is 0.08. what is the probability that if one pints of blood is taken from each of 100 unrelated blood donors fewer than three pints of group B blood will be obtained?

To find the probability of obtaining fewer than three pints of group B blood, we need to consider the probability of obtaining zero, one, or two pints of group B blood and then sum them up.

Let's start by calculating the probability of obtaining exactly zero pints of group B blood. Given that the probability of having blood group B is 0.08, the probability of not having blood group B (having a different blood group) is 1 - 0.08 = 0.92.

The probability of obtaining zero pints of group B blood from one donor can be calculated using the binomial probability formula:

P(X=k) = nCk * p^k * (1-p)^(n-k),

where:
P(X=k) is the probability of obtaining k successes,
n is the number of trials or donors (in this case, 1),
k is the number of successful outcomes (0 in this case),
p is the probability of success (0.92 in this case), and
(1-p) is the probability of failure.

Plugging the values into the formula:

P(X=0) = 1C0 * 0.92^0 * (1-0.92)^(1-0)
= 1 * 1 * (0.08)
= 0.08

So, the probability of obtaining zero pints of group B blood from one donor is 0.08.

Next, let's calculate the probability of obtaining exactly one pint of group B blood. Using the same binomial probability formula:

P(X=1) = 1C1 * 0.08^1 * (1-0.08)^(1-1)
= 1 * 0.08 * 1
= 0.08

The probability of obtaining one pint of group B blood from one donor is also 0.08.

Finally, let's calculate the probability of obtaining exactly two pints of group B blood.

P(X=2) = 1C2 * 0.08^2 * (1-0.08)^(1-2)
= 0 (since the probability of obtaining two pints of group B blood from one donor is negligible)

Now, we can calculate the probability of obtaining fewer than three pints of group B blood by summing up the individual probabilities we calculated:

P(fewer than three pints of group B blood) = P(X=0) + P(X=1) + P(X=2)
= 0.08 + 0.08 + 0
= 0.16

Therefore, the probability that if one pint of blood is taken from each of 100 unrelated blood donors, fewer than three pints of group B blood will be obtained is 0.16.