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

Question

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

in progress 0
Vodka 2 months 2021-08-19T05:32:25+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-19T05:33:35+00:00

    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:

    P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

    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:

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

    C_{n,x} = \frac{n!}{x!(n-x)!}

    In this question:

    45 boxes, which means that N = 45

    22 have the secret decoder ring, which means that k = 22

    Two boxes, which means that n = 2

    What is the probability that both of them have the secret decoder ring?

    This is P(X = 2). So

    P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

    P(X = 2) = h(2,45,2,22) = \frac{C_{22,2}*C_{23,0}}{C_{45,2}} = 0.2333

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

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )