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10 April, 11:33

Assume that when an adult is randomly selected, the probability that they do not require vision correction is 23 %. If 6 adults are randomly selected, find the probability that exactly 2 of them do not require a vision correction.

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  1. 10 April, 11:52
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    P (X = 2) = 0.27894

    Step-by-step explanation:

    Given:

    - The probability that no vision correction is required p = 0.23

    - No. adults are randomly selected n = 6

    Find:

    - P (Exactly 2 dont require vision correction)

    Solution:

    - We will declare a random variable X is the umber of adults out of 6 that do not require vision correction. X follows a Binomial distribution:

    X~ B (6, 0.23)

    - The probability required is P (X = 2)

    - Using the pmf of binomial distribution we have:

    P (X = 2) = 6C2 * (0.23) ^2 * (0.77) ^4

    P (X = 2) = 15 * 0.0529 * 0.35153041

    P (X = 2) = 0.27894
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