Question

Approximately 2.5% of the eggs in a store are cracked. If you buy two dozen eggs, what is the probability that: (show all work and round to 3 decimal places) a) at least one of your eggs is cracked For the toolbar, press ALT+F10 (PC) Or ALTFN+F10 (Mac).

Answer 1

To find the probability of getting at least one cracked egg when purchasing two dozen eggs with a 2.5% chance of each egg being cracked, we use the complement rule and calculate 1 - (0.975)^24, resulting in approximately 0.540 after rounding to three decimal places.

Step-by-step explanation:

To calculate the probability of getting at least one cracked egg when buying two dozen eggs, given that approximately 2.5% of the eggs are cracked, we use the complement rule. This rule states that the probability of 'at least one' is equal to 1 minus the probability of 'none'.

Let's first find the probability of getting no cracked eggs when buying one egg. Since 2.5% are cracked, the probability of one egg being not cracked is 1 - 0.025 = 0.975.

Buying two dozen eggs means buying 24 eggs. The probability of all 24 eggs being not cracked is 0.975^24.

P(no cracked eggs) = 0.97524

Now, we calculate the probability of at least one cracked egg by subtracting the above probability from 1.

P(at least one cracked egg) = 1 - P(no cracked eggs) = 1 - 0.97524 = 1 - 0.460

Let's round the result to three decimal places:

P(at least one cracked egg) ≈ 0.540