aron flips a penny 9 times. which expression represents the probability of getting exactly 3…

aron flips a penny 9 times. which expression represents the probability of getting exactly 3 heads?\n$p(k\text{ successes}) = _nc_kp^k(1 - p)^{n - k}$\n$_nc_k=\frac{n!}{(n - k)!k!}$\n$\\circ _9c_3(0.5)^3(0.5)^6$\n$\\circ _9c_3(0.5)^3$\n$\\circ _9c_3(0.5)^3(0.5)^9$\n$\\circ _9c_6(0.5)^6$

aron flips a penny 9 times. which expression represents the probability of getting exactly 3 heads?\n$p(k\text{ successes}) = _nc_kp^k(1 - p)^{n - k}$\n$_nc_k=\frac{n!}{(n - k)!k!}$\n$\\circ _9c_3(0.5)^3(0.5)^6$\n$\\circ _9c_3(0.5)^3$\n$\\circ _9c_3(0.5)^3(0.5)^9$\n$\\circ _9c_6(0.5)^6$

Answer

Explanation:

Step1: Identify values for formula

The binomial - probability formula is (P(k\text{ successes})={}{n}C{k}p^{k}(1 - p)^{n - k}), where (n) is the number of trials, (k) is the number of successes, and (p) is the probability of success on a single trial. Here, (n = 9) (number of coin - flips), (k = 3) (number of heads), and for a fair coin (p=0.5) (probability of getting a head on a single flip), and (1 - p = 0.5).

Step2: Substitute values into formula

Substitute (n = 9), (k = 3), and (p = 0.5) into the formula. We get (P(3\text{ heads})={}{9}C{3}(0.5)^{3}(1 - 0.5)^{9 - 3}={}{9}C{3}(0.5)^{3}(0.5)^{6}).

Answer:

({}{9}C{3}(0.5)^{3}(0.5)^{6}) (corresponding to the first option in the multiple - choice list)