Question

At the Petite École Internationale Day Care, the diapers are changed every 2 hours. The day care workers believe 15% of the diapers leak before they are changed. When the diapers are changed, about 70% are full. The workers have noticed that of the diapers that are full, around 20% leak. Given that a diaper has leaked, what is the probability that the diaper is full?

Answer 1

Answer: The probability that the diaper is full given that it has leaked is 0.105.

Answer 2

The probability that the diaper is full given that it has leaked is 0.105

Explanation:

The given parameters are;

The percentage of diapers that leak before they are changed = 15%

The percentage of diapers that are full when they get changed = 70%

The percentage of full diapers that that leak = 20%

Therefore, given that the percentage of the changed diapers that are full = 70% and out of the full diapers that leak = 20%

∴ The probability that the diaper is full given that it has leaked = The percentage of diapers that leak before they are changed × The percentage of diapers that are full when they get changed

The probability that the diaper is full given that it has leaked = 15/100 × 70/100 = 21/200 = 0.105

The probability that the diaper is full given that it has leaked = 0.105