assume that a reseacher randomly selected 14 new born babies and counts the number of girls selected x. the probability corresponding to the 14 possible values of x. find the probability of selecting exactly 8 girls.
To find the probability of selecting exactly 8 girls out of 14 newborn babies, we first need to determine the total number of possible outcomes.
In this scenario, each newborn baby can either be a girl or a boy, so there are two possible outcomes for each baby. Since there are 14 babies in total, the total number of possible outcomes is 2^14 = 16,384.
Next, we need to determine the number of favorable outcomes, which is the number of ways we can select exactly 8 girls out of the 14 babies.
To calculate this, we can use the binomial coefficient formula: nCr = n! / (r!(n-r)!)
In this case, n represents the total number of babies (14) and r represents the number of girls (8).
Using the formula, we can calculate the number of ways to select 8 girls out of 14 babies:
nCr = 14! / (8!(14-8)!) = 14! / (8!6!) = (14*13*12*11*10*9*8!) / (8!6!) = (14*13*12*11*10*9) / (6*5*4*3*2*1) = 3003
Therefore, there are 3003 possible ways to select exactly 8 girls out of 14 newborn babies.
Finally, we can calculate the probability of selecting exactly 8 girls by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 3003 / 16384 ≈ 0.1831
So, the probability of selecting exactly 8 girls out of 14 newborn babies is approximately 0.1831, or 18.31%.