In a particular lottery, 5 winning numbers are drawn from a set of 37 numbers. What is the probability of picking exactly 2 of the winning n

Question

In a particular lottery, 5 winning numbers are drawn from a set of 37 numbers. What is the probability of picking exactly 2 of the winning numbers in this lottery? Round your answer to the nearest
thousandth (three decimal places).

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King 6 days 2021-07-22T23:48:13+00:00 1 Answers 2 views 0

Answers ( )

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    2021-07-22T23:49:57+00:00

    Since 5 winning numbers are draw and there are exactly 2 winning numbers, the other 3 numbers chosen have to be incorrect.

    The 2 numbers picked right, there are 5C2=10 different possibilities.

    The other 3 numbers are just picked from the rest of the 32 numbers. Getting there are 32C3=4960 different possibilities.

    For each set of 2 correct winning numbers, you could have the 4960 different losing numbers to match up to make a unique set. This meant that there are 4690*10=46900 different total possibilities.

    Now the total different outcomes of how you can choose the numbers are 37C5=435897 outcomes.

    Now the way to find probabilities is want/total

    The want is 46900 and the total is 435897

    Doing the division you get the number rounded to the nearest thousandths as   0.107 or in percent form as

    10.759% chance of picking exactly 2 winning numbers.

    This seems like a competition problem of some sort therefore I assume that you already know what combinations in form nCk and permutation in form nPk means.

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