A box holds 240 eggs. The probability that an egg is brown is 0.05. How do you find the probability that there are 15 brown eggs in the box?
Improbable.
The box has 0.05 X 240 = 12 brown eggs only. The probability of finding more than 12 brown eggs is 0.
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You can use the binomial probability formula to find the probability of getting a specific number of successes in a fixed number of independent trials.
The formula is: [ P(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} ]
Where:
- ( n ) is the number of trials (eggs in the box)
- ( k ) is the number of successes (brown eggs)
- ( p ) is the probability of success (probability that an egg is brown)
- ( \binom{n}{k} ) is the binomial coefficient, calculated as ( \frac{n!}{k!(n-k)!} )
Given:
- ( n = 240 )
- ( k = 15 )
- ( p = 0.05 )
Plug in the values and calculate: [ P(X = 15) = \binom{240}{15} \times (0.05)^{15} \times (1-0.05)^{240-15} ]
Calculate ( \binom{240}{15} ) using a calculator or software. Then, compute ( (0.05)^{15} ) and ( (1-0.05)^{240-15} ), and multiply them together.
This will give you the probability that there are exactly 15 brown eggs in the box.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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