Question

Cans of frozen orange juice are weighed to ensure they are not underfilled. Cans are independent, and the probability that a can is underfilled is 0.024. Three cans are weighed sequentially. What is the probability that all three cans are not underfilled

Answer 1

Answer: 0.999986176

Step-by-step explanation:

To solve this, the probability distribution formula for selection will be used

Where P(x=r) = nCr * p^r * q^n-r

To get the probability that all 3cans are not overfilled, since the probability of success given in the question is that of a can being overfilled, then we will first derive the probability of having exactly 3cans being overfilled and subtract this gotten answer from 1

n= 3, r=3, p=0.024, q=1-0.024=0.976

When, 3 cans are overfilled, P(x=3) becomes:

P(x=3) = 3C3 * 0.024^3 * 0.976^0

P(x=3) = 1 * 0.000013824 * 1

P(x=3) = 0.000013824.

Then, probability that all three cans are not overfilled becomes :

1 - 0.000013824. = 0.999986176,