What is the probability of flipping a coin 75 times and getting tails 35 times or fewer? Round your answer to the nearest tenth of a percent. A. 99.7% B. 32.2% C. 5.3% D. 75.6%

Accepted Solution

Let X be the number of tail when a coin is flipped n number of times. Let n is the number of times a coin is flipped. Let p be the probability of getting tail on any flip of coin.Here as coin is fair coin the chance of getting head or tail at any flip is 1/2.n=75, p =0.5 From given information X follows Binomial distribution with n=75 and p=0.5The probability that getting tail 35 or fewer times isP(X ≀ 35) = P(X=35) + P(X=34) + P(X=33) + ....+ P(X=2) + P(x=1)The Binomial probability is calculated using probability function[tex] P(X=k) = (nCk) p^{k} (1-p) ^{n-k} [/tex]For given parameters n=75 and p=0.5 the probability of getting X=k is[tex] P(X=k) = (75Ck) 0.5^{k} (1-0.5) ^{75-k} [/tex]Using excel function to find cumulative binomial probability for x=1 to 35 is=BINOM.DIST(35,75,0.5,1) = 0.322The probability there will be 35 or fewer tails is 0.322The percentage of getting 35 or fewer tails is 32.2%