Zara is about to start a new job and must complete a first aid course as part of her training.
At the end of the first aid course there is a test which is split into two parts, a theory test and a practical test.
The probability of passing the theory test is 0.75.
The probability of passing only one of the two parts is 0.36.
The two events are independent.
Work out the probability of passing the practical test.
Answer:
The probability of passing the theory test is 0.75, and so to fail is 0.25.
The probability of passing the practical test is x, and so to fail is (1-x) since all probabilities add up to 1.
The combination of outcomes are:
Pass Theory + Pass Practical
Pass Theory + Fail Practical
Fail Theory + Pass Practical
Fail Theory + Fail Practical
Only 2 out of the 4 combinations fit the criteria for only 1 test passed, therefore we can form an equation.
0.75(1-x) + 0.25x = 0.36
Now solve to find x…
0.75 – 0.75x + 0.25x = 0.36
0.75 – 0.5x = 0.36
0.39 = 0.5x
x = 0.78