A recent survey showed that 64% of college students drink coffee daily.Find the probability that three of the next four students that come to class will drink coffee daily. Find the probability that more than five of the next ten students to come to class will drink coffee daily.

Name: A recent survey showed that 64% of college students drink coffee daily
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: A recent survey showed that 64% of college students drink coffee daily.Find the probability that three of the next four students that come to class will drink coffee daily. Find the probability that more than five of the next ten students to come to

Given information: Probability of college students drinking coffee daily p=0.641. Let X be the college students that drink coffee daily. X~Binomialn,p Then, probability of x number of students drinking coffee daily out of n given students is: PX=x=Cx×n0.64x×1-0.64n-x=Cxn×0.64x×0.36n-x In this case, n=4. Therefore, the probability that three of the next four students that come to class will drink coffee daily can be calculated as follows: PX=3=C34×0.643×0.364-3=4×0.643×0.361=0.3775 Therefore, the required probability is 0.3775.2. In this case, n=10. Therefore, the probability that more than five of the next ten students to come to class will drink coffee daily can be calculated as follows: PX>5=PX≥6=PX=6+PX=7+PX=8+PX=9+PX=10=C610×0.646×0.3610-6+.....+C1010×0.6410×0.3610-10=0.7292 Therefore, the required probability is 0.7292.