The probability of being born with condition A is 0.10 and the probability of being born with condition B is 0.50. If condition A and B are independent , what is probability of being born with either condition A or condition B ( or both)? (AIIMS may 2012)
Ref: High Yield Biostatistics, Pg: 2-3
For two events or conditions, the probability that either will occur is the sum of their probabilities, minus the probability that both will occur. This is illustrated in the following figure:
- If we simply add the probability of A to the probability of B, the area labeled “A and B” will get counted twice.
- Therefore, the probability of (A and B) must be subtracted from the sum of the probabilities: p(A or B) = p(A) + p(B) — p(A and B). In this question, it is specifically stated that the two conditions are independent.
- When that is the case, the probability that both will occur is the product of their probabilities: p(A and B) = p(A) X p(B). The answer to this problem is 0.1 + 0.5 — (0.1)(0.5) = 0.55. Note that another common situation is when two conditions are mutually exclusive rather than independent (i.e., the probability that both will occur is zero).
- In this case, the probability that either one will occur is simply the sum of their probabilities. For example, if condition A were blue eyes and condition B brown eyes, the probability of either blue or brown eyes would be 0.60.