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,
