My idea is that by finding the combination of arranging the 10 bears into the sample, this can be us

qtbabe9876a9

qtbabe9876a9

Answered question

2022-05-19

My idea is that by finding the combination of arranging the 10 bears into the sample, this can be used to calculate the probability. For example, this would be 10 C 5 = 30240. However, how would I calculate the number of arrangements of the four bears that will go into the sample? I considered 5 C 4 , yet this would be illogical as it only includes the number of arrangements of the four bears in the sample, but does not consider the arrangements in the sample not selected. Is my working correct?

Answer & Explanation

Julien Carrillo

Julien Carrillo

Beginner2022-05-20Added 13 answers

The first part is correct. You will need 10 C 5 , as this is the total number of combinations of picking 5 bears out of 10. But the second part starts to go awry. We are not interested in 5 C anything because it looks like the 5 is referring to what you already selected. This is generally not the way to go. Instead, you need to find the probability that 1 pregnant mother is in the sample, 2, 3, or all 4. This is 4 C 1 6 C 4 + 4 C 2 6 C 3 + 4 C 3 6 C 2 + 4 C 4 6 C 1 10 C 5 , where each term in the numerator represents choosing however many pregnant mother bears times choosing however many male or not pregnant mother bears. Divide this all by the number of ways to choose 5 bears out of 10.
It is easier to think of the complement, one minus the probability of selecting no pregnant mother bears. 1 6 C 5 10 C 5 . This is the same as adding up all the terms above.

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