Exercise
1. If you have a case where n=25 and P=0.04, what is the probability that x is equal to 4?

If [tex]n=25[/tex] and [tex]p=0.04[/tex], then the probability of [tex]P(X=4)[/tex] is found to be 0.001374.What is Binomial Distribution?In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability, [tex]p[/tex]) or failure (with probability, [tex]q=1-p[/tex]).How to Find the Probability of a Binomial Distribution?The chance of failure raised to the power of the difference between the number of tries and the number of successes is multiplied by the probability of success raised to the power of the number of successes in order to compute the binomial distribution. Next, multiply the final result by the sum of the number of attempts and the number of successes.The formula for binomial distribution is given as, [tex]P(X=k)={n \choose k}p^{k}(1-p)^{n-k}[/tex]From the given question, we have, [tex]n=25[/tex] and [tex]p=0.04[/tex]Here, have to find the probability of [tex]P(X=4)[/tex], so [tex]k=4[/tex]The binomial distribution formula is, [tex]P(X=k)={n \choose k}p^{k}(1-p)^{n-k}[/tex]Substituting the given values in the above equation, we get[tex]P(X=4)={25 \choose 4}0.04^{4}(1-0.04)^{25-4}[/tex][tex]\implies P(X=4)=12650 \times0.00000256\times0.4243\\\implies P(X=4)=0.001374[/tex]Therefore, the value of [tex]P(X=4)=0.001374[/tex]To learn more about binomial distribution from the given linkhttps://brainly.com/question/15246027#SPJ1