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?

Answer 1

Improbable.

0.05 = (the count of brown eggs in the box)#/#(the total number of egg in the box) = (the count of brown eggs in the box)#/#240.

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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Answer 2

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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Answer from HIX Tutor

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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