If the probability that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year, is

Options

A. p+q
B. p+q-2pq
C. p+q-pq
D. p+q+pq

Answer

To find the probability that only one of A or B will be alive at the end of the year, we can follow these steps:

### Step 1: Define the probabilities
Let:
- \( p \) = Probability that A will die within a year.
- \( q \) = Probability that B will die within a year.

From this, we can also define the probabilities of A and B being alive:
- Probability that A is alive = \( 1 - p \)
- Probability that B is alive = \( 1 - q \)