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Sagot :
Answer:
31.82% probability that you will receive 2 apples.
Step-by-step explanation:
The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
5 + 7 = 12 total fruits, which means that [tex]N = 12[/tex]
7 apples, which means that [tex]k = 7[/tex]
You receive 2 fruits, which means that [tex]n = 2[/tex]
What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?
This is, as a proportion, P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182[/tex]
0.3182*100% = 31.82%
31.82% probability that you will receive 2 apples.
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