To solve the problem, we need to determine the probabilities and subsequently compute the combined probability for three donations being suitable for a person with type A blood.
Here are the steps to reach the solution:
1. Understand the Problem: We are given the percentages of different blood types in blood banks, and we know that a person with type A blood can receive both type A and type O blood.
- Type O: [tex]\(49\% = 0.49\)[/tex]
- Type A: [tex]\(27\% = 0.27\)[/tex]
- Type B: [tex]\(20\% = 0.20\)[/tex]
- Type AB: [tex]\(4\% = 0.04\)[/tex]
2. Identify Relevant Probabilities: For a type A blood recipient, we focus on type A and type O blood.
3. Calculate Combined Probability for Type A and Type O: To find the probability that a single donation is either type A or type O, we sum the probabilities of these two events.
[tex]\[
P(\text{type A or type O}) = P(\text{type A}) + P(\text{type O}) = 0.27 + 0.49 = 0.76
\][/tex]
4. Calculate the Probability for Three Donations: We need the probability that all 3 out of 3 donations can be used for a type A recipient. Since we assume independence of donations, we raise the combined probability to the power of 3.
[tex]\[
P(\text{all 3 donations can be used}) = (P(\text{type A or type O}))^3 = 0.76^3
\][/tex]
5. Compute the Final Probability:
[tex]\[
0.76^3 = 0.438976
\][/tex]
Thus, the probability that all 3 donations can be safely used for someone with type A blood is approximately [tex]\(0.4390\)[/tex].
