Question

the binomial formula gives us a way to calculate the probability without having to draw out the tree diagram. binomial formula $p(x)=\binom{n}{k}p^{k}(1 - p)^{n - k}$ where: n is the __ of trials p is the of success k is the of successes. lets look again at our example with the three coins. example 2: suppose i flip three coins. i want to know the probability i get two heads and one tail. a. identify what n, p, and k are in this situation. p: n: k: __ b. now fill in the formula with the appropriate amounts and use the calculator to get your answer. c. how does this value compare to the answer you got in example 1?

Explanation:

Step1: Identify variables for coin - flip

n is number of flips, p is prob of head, k is num of heads. So n = 3, p = 0.5, k = 2.

Step2: Apply binomial formula

$P(X)=\binom{3}{2}(0.5)^{2}(1 - 0.5)^{3 - 2}=\frac{3!}{2!(3 - 2)!}\times(0.5)^{2}\times(0.5)^{1}=3\times0.25\times0.5 = 0.375$

Answer:

a. p: 0.5, n: 3, k: 2
b. 0.375
c. No info about example 1, can't answer.