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Question

Consider n independent trials of an experiment in which each trial has two possible outcomes, success or failure. The probability of a success on each trial is p and the probability of a failure is q = 1 - p. In this context, the term $_{n} C_{k} p^{k} q^{n-k}$ in the expansion of $(p+q)^{n}$ gives the probability of k successes in the n trials of the experiment. A fair coin is tossed seven times. To find the probability of obtaining four heads, evaluate the term $_{7} C_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{3}$ in the expansion of $\left(\frac{1}{2}+\frac{1}{2}\right)^{7}$.

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In this task we have to calculate the probability of obtaining four heads after a fair coin is tossed seven times which we can find by evaluating the term

$_{7}C_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{3}$

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