If you were to flip a coin 10 times, what is the probability that it will land on heads exactly 7 out of 10 times? Pls show wor

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If you were to flip a coin 10 times, what is the probability that it will land on heads exactly 7 out of 10 times?

Pls show work.

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Trung Dũng 4 years 2021-08-22T00:51:49+00:00 1 Answers 6 views 0

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  1. Orla
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    2021-08-22T00:53:31+00:00
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    Answer:

    The probability of flipping a coin 10 times and it landing on heads exactly seven times is about 0.1172 or 11.72%.

    Step-by-step explanation:

    We can use basic binomial distribution, which is given by the formula:

    \displaystyle P(x) = {n \choose x}p^xq^{n-x}

    Where n represent the number of trials, x represent the number of successes desired, p represent the chance of success, and q represent the chance of failure.

    Since we are flipping a coin 10 times, we are conducting 10 trials. So, n = 10.

    We want to probability that it lands on heads exactly 7 out of 10 times. So, the number of desired successes x is 7.

    The probability of success p is 1/2.

    And the probability of failure q is also 1/2.

    Substituting:

    \displaystyle P(7)={10 \choose 7}\left(\frac{1}{2}\right)^7\left(\frac{1}{2}\right)^3=120\left(\frac{1}{2}\right)^{10}=\frac{120}{1024}=\frac{15}{128}\approx0.1172

    The probability of flipping a coin 10 times and it landing on heads exactly seven times is about 0.1172 or 11.72%.

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