5. (1 point) 98 percent of all babies survive delivery. However, 15 percent of all births

involve Cesarean (C) sections. When a C section is performed the baby survives 96% of

the time. If a randomly chosen pregnant woman does not have a C section, what is the probability that her baby survives? 6. (1 point) Let X represent the difference between the number of heads and the number

of tails obtained when a coin is tossed 'n, times. What is the support of X? 0,1,2,...,n—2,n—1,n

0,1,2,...,2n—2,2n—1,2n

0,2,4,...,n—4,n—2,n

—n,n+1,n+2...,n—2,n—1,n E. —n,—n+2,—n+4,...,n—4,n—2,n 5.0173? 7. A fair die is rolled 10 times.

(a) (1 point) What is the probability that it shows the number 4 exactly 5 times?

(b) (1 point) What is the appropriate R code for calculating the probability from part (a)?

(c) (1 point) What is the probability that we roll an even number at least once? (d) (1 point) Which of the following lines of code does not produce the probability

asked for in part c? A. 1 — choose(10,0)*(0.5)‘0*(1—0.5)‘(10)

B. 1 — dbinom(0, 10, 0.5) C. pbinom(0,10,0.5) D. pbinom(0,10,0.5, lower.tail = FALSE) (e) (1 point) What is the probability that it shows the number 3 no more than 5 times?

(I highly reccommend that you calculate this in R to avoid making any errors) 8. (1 point) Suppose that a box of 100 toys contains 6 that are broken. If X is the number

of broken toys selected in a random sample of 10 toy from the box, ﬁnd P(X > 2).