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## Inside the box of every cereal box contains a surprise gift. The store manager assures employees that 22 of the 45 boxes on the shelf have a

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Inside the box of every cereal box contains a surprise gift. The store manager assures employees that 22 of the 45 boxes on the shelf have a secret decoder ring and inside the other 23 boxes on the shelf contain a different gift. If two cereal boxes are randomly selected from the shelf to purchase, what is the probability that both of them have the secret decoder ring

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Mathematics
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2021-08-19T05:32:25+00:00
2021-08-19T05:32:25+00:00 1 Answers
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## Answers ( )

Answer:0.2333 = 23.33% probability that both of them have the secret decoder ring

Step-by-step explanation:The cereals are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:The probability of x successes is given by the following formula:

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:45 boxes, which means that

22 have the secret decoder ring, which means that

Two boxes, which means that

What is the probability that both of them have the secret decoder ring?This is P(X = 2). So

0.2333 = 23.33% probability that both of them have the secret decoder ring