bag contains 9 real diamonds and 5 fake diamonds. if 9 diamonds are picked from the bag at random, what is the probability that all of them are real?

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01-12-2022
Mathematics

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bag contains 9 real diamonds and 5 fake diamonds. if 9 diamonds are picked from the bag at random, what is the probability that all of them are real?

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fahiskt9087 fahiskt9087 · Answer 1 · 2022-12-06T18:26:38+01:00

The probability that all of them are real is 0.01875 or 1.875%

If the diamonds are replaced after each draw:

The probability of drawing a real diamond is 9/14, found by making the numerator the number of real diamonds and adding the total number of diamonds to find the denominator. 5+9 = 14.

To find the probability of all 9 diamonds drawn being real, multiply 9/14 by itself 9 times. = 387420489/ 20661046784. This creates a probability of 387420489/ 20661046784. This cannot be reduced because there is no common factor. To express as a decimal, divide. 387420489/ 20661046784 = 0.01875. To turn this into a percent, multiply by 100. 0.01875*100 = 1.875

Hence, the probability that all of them are real is 0.01875 or 1.875%

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