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15 November, 06:20

Anna is learning how to do a back flip. She is successful 50% of the time. As her gymnastics competition approaches, Anna practices every day. The day before competition she would like to determine the probability of completing her back flip successfully 8 out of 10 times. Design a simulation that Anna could use in this situation.

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  1. 15 November, 08:12
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    P (8; 10, 0.50) = 4.39%

    There is 4.39% probability that Anna will complete her back flip successfully 8 out of 10 times.

    Step-by-step explanation:

    The given problem can be modeled as a binomial experiment since the following conditions are satisfied.

    • There are n repeated trials and are independent of each other.

    • There are only two possibilities: Anna is successful in doing a back flip or Anna is unsuccessful in doing a back flip.

    • The probability of success does not change with trial to trial.

    The binomial distribution is given by

    P (x; n, p) = nCx pˣ (1 - p) ⁿ⁻ˣ

    Where p is the probability that Anna is successful in doing a back flip and 1 - p is the probability that Anna is unsuccessful in doing a back flip, n is number of trials and x is the variable of interest.

    In this case, we have x = 8, n = 10 and p = 0.50

    P (8; 10, 0.50) = (10C8) * (0.50) ⁸ * (1 - 0.50) ¹⁰⁻⁸

    P (8; 10, 0.50) = (45) * (0.50) ⁸ * (0.50) ²

    P (8; 10, 0.50) = 0.0439

    P (8; 10, 0.50) = 4.39%

    Therefore, there is 4.39% probability that Anna will complete her back flip successfully 8 out of 10 times.
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