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11 May, 03:15

johnny has a 70% chance of passing a test. If johnny has 4 tests this year, what is the probability that johnny passes all of his tests?

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  1. 11 May, 03:41
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    The probability that johnny passes all of his tests (4) is 24.01%

    Step-by-step explanation:

    Let's recall that the binomial distribution is defined completely by its two parameters, n (number of trials) and p (probability of success). In our question, n = 4 and p = 0.7.

    Also let's recall that the formula for finding the probability of x exact number of successes in n trials is:

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

    Where:

    b = binomial probability

    x = total number of "successes" (pass or fail, heads or tails etc.)

    P = probability of a success on an individual trial

    n = number of trials

    Using the formula above, we can elaborate our binomial distribution table, as follows:

    Binomial distribution (n=4, p=0.7)

    x Pr[X = x]

    0 0.0081 0.81%

    1 0.0756 7.56%

    2 0.2646 26.46%

    3 0.4116 41.16%

    4 0.2401 24.01%

    Therefore, the probability that johnny passes all of his tests (4) is 24.01%
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