Question

Assume that a researcher randomly selects 14 newborn babies and counts the number of girlsâ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting 9 or more girls.

Answer 1

Probability is the mathematics of chance. In other words, it is the fraction or percentage of a certain event successfully happening. For this problem, you want to determine the probability of selecting 9, 10, 11, 12, 13 or 14 girls. The solution is as follows:

P = nCr p^r q^n-r
where 
n is number of total events (n = 14)
r is the number of events that could happen (9, 10, 11, 12 ,13 and 14)
p is the probability of an event being a girl (p = 50% or 0.5)
q is the probability of either an event being a boy (q = 1-p = 0.5)
nCr is a combination formula which is n!/(r!(n-r)!)

P = [14C9* (.5)^9 * (0.5)^5]+ [14C10* (.5)^10 * (0.5)^4]+[14C11* (.5)^11 * (0.5)^3]+[14C12* (.5)^12 * (0.5)^2]+[14C13* (.5)^13 * (0.5)^1]+[14C14* (.5)^14 * (0.5)^0]

P = 0.211 or 21.1%