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Zarrin [17]
2 years ago
9

In a certain​ college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the phy

sics​ majors, what is the probability that no more than 6 belong to an ethnic​ minority? Round to three decimal places.
Mathematics
1 answer:
kipiarov [429]2 years ago
8 0

Answer:

0.073

Step-by-step explanation:

Given information:

Probability of ethnic minorities (P) = 0.33

Number of Trials (n) = 10

Required successes (x) = 6 or more

To find the answer for this problem we will employ the Binomial Probability equation

b(x; n, P) = nCx * P^x * (1-P)^n^-^x

To find the answer for 6 or more success we first calculate the following values

1) 6 success

2) 7 success

3) 8 success

4) 9 success

5) 10 success

so

b6 = 10C6 * (0.33)^6 * (1-0.33)^1^0^-^6 = 0.0547

b7 = 10C7 * (0.33)^7 * (1-0.33)^1^0^-^7 = 0.0154

b8 = 10C8 * (0.33)^8 * (1-0.33)^1^0^-^8 = 2.841 * 10^-^3

b9 = 10C9 * (0.33)^9 * (1-0.33)^1^0^-^9 = 3.110 * 10^-^4

b10 = 10C10 * (0.33)^10 * (1-0.33)^1^0^-^10 = 1.532 * 10^-^5

Adding all these values we get the probabilities we get 0.0732

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