A first aid test has two parts, a theory test and a practical test.The probability of passing the theory test is 0.75The probability of passing only one of the two parts is 0.36The two events are independent.Work out the probability of passing the practical test

Given that the probability of passing only one of the two parts is 0.36 and the probability of passing the theory test is 0.75, we can use these two pieces of information to find the probability of passing the practical test.

The probability of passing only one of the two parts can be broken down into two scenarios: passing the theory but failing the practical, and failing the theory but passing the practical. Since the two events are independent, the probability of each scenario is the product of the probabilities of the individual events.

So, the probability of passing the theory but failing the practical is (probability of passing theory) * (probability of failing practical) = 0.75 * (1 - P(practical)), where P(practical) is the probability of passing the practical test.

Similarly, the probability of failing the theory but passing the practical is (probability of failing theory) * (probability of passing practical) = (1 - 0.75) * P(practical).

Since the probability of passing only one of the two parts is the sum of these two probabilities, we have:

0.36 = 0.75 * (1 - P(practical)) + (1 - 0.75) * P(practical)

Solving this equation for P(practical), we get:

P(practical) = (0.36 - 0.75 * 0.25) / (0.75 + 0.25) = 0.3

So, the probability of passing the practical test is 0.3.