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%
The value on n is simply the number of values or the size of the sample data. In our case, we have a total of 8 data values. The value of n will thus be 8
