Question

there are four blood types, and not all are equally likely to be in blood banks. in a certain blood bank, 49% of donations are type o blood, 27% of donations are type a blood, 20% of donations are type b blood, and 4% of donations are type ab blood. a person with type b blood can safely receive blood transfusions of type o and type b blood. what is the probability that the 4th donation selected at random can be safely used in a blood transfusion on someone with type b blood? (0.31)^3(0.69) (0.51)^3(0.49) (0.69)^3(0.31) (0.80)^3(0.20)

Explanation:

Step1: Calculate the probability of non - safe blood

The probability of a donation being safe for Type B (Type O or Type B) is \(P(\text{safe})=0.49 + 0.20=0.69\). The probability of a donation being non - safe for Type B (Type A or Type AB) is \(P(\text{non - safe})=1 - 0.69 = 0.31\).

Step2: Use the probability formula for the 4th trial

We want the first 3 donations to be non - safe and the 4th to be safe. Since each donation is an independent event, the probability is \(P=(0.31)^{3}(0.69)\)

Answer:

\((0.31)^{3}(0.69)\)