Compute the following binomial probabilities directly from the formula for b(x; n, p):

a. b(3; 8, .35)
b. b(5; 8, .6)
c. p(3< =x< =5) when n=7 and p = .6
d. p(1 < = x) when n=9 and p= .1

B(x; n, p) = nCx(p^x * (1 - p)^(n - x))

a.) b(3; 8, .35) = 8C3(0.35^3 * 0.65^5) = 56 x 0.042875 x 0.116029 = 0.2786

b.) b(5; 8, .6) = 8C5(0.6^5 * 0.4^3) = 56 x 0.07776 x 0.064 = 0.2787

c.) P(3 <= x <= 5) = P(3) + P(4) + P(5) = 7C3(0.6^3 * 0.4^4) + 7C4(0.6^4 * 0.4^3) + 7C5(0.6^5 * 0.4^2) = (35 x 0.216 x 0.0256) + (35 x 0.1296 x 0.064) + (21 x 0.07776 x 0.16) = 0.193536 + 0.290304 + 0.2612736 = 0.7451

The answer is c. 7 (i think) i’m almost sure though