Question

using the multiplication rule for independent events
jocelyn boils 24 eggs. from experience, she knows that the shell of any given egg has a 0.04 probability of cracking during the boiling process. if shells crack independently, what is the probability that at least 1 egg will come out of the boiling process with a cracked shell?
round to 2 decimal places.

Explanation:

Step1: Find the probability of an egg not cracking

The probability of an egg cracking is \(p = 0.04\). The probability of an egg not cracking is \(q=1 - p\).
So, \(q = 1-0.04=0.96\)

Step2: Use the multiplication rule for independent events

Since there are \(n = 24\) eggs and the events (eggs not cracking) are independent, the probability that all \(24\) eggs do not crack is \(P(\text{no cracks})=q^{n}\).
Substitute \(n = 24\) and \(q = 0.96\) into the formula: \(P(\text{no cracks})=(0.96)^{24}\)

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Step3: Find the probability of at least one crack

The probability of at least one crack is \(P(\text{at least one crack}) = 1-P(\text{no cracks})\)
Substitute \(P(\text{no cracks})\approx0.375\) into the formula: \(P(\text{at least one crack})=1 - 0.375 = 0.625\approx0.63\)

Answer:

\(0.63\)