## Related questions with answers

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. The probability of a baseball player getting a hit during any given time at bat is $\frac{1}{4}$. To find the probability that the player gets three hits during the next 10 times at bat, evaluate the term $_{10} \mathrm{C}_{3}\left(\frac{1}{4}\right)^{3}\left(\frac{3}{4}\right)^{7}$ in the expansion of $\left(\frac{1}{4}+\frac{3}{4}\right)^{10}$

Solution

VerifiedIn this task we have to calculate the probability that the player gets three hits during the next $10$ times at bat which we can find by evaluating the term

$_{10}C_{3}\left(\frac{1}{4}\right)^{3}\left(\frac{3}{4}\right)^{7}$

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