## Question 405:

Asked on September 22, 2008

Tags:
Multiplication Rule ,
BINOMDIST ,
Gambler's Fallacy ,
Probability Mass Function

1

## Answer:

No answer provided yet.

- Their reasoning, while understandable is not accurate because each birth is an independent event. That is, the next child being born doesn't know that there are 5 girls. This is like saying the roulette wheel is due to come up black, since the last 5 were red (called the Gamblers Fallacy).
- Let's assume that the odds of having a boy or girl are equal, or 50/50 (this might not be the case biologically, but we'll assume it is for these questions). We can get the probability of independent events happing together or in total by multiplying their individual probabilities. This is called the multiplication rule. So the probability of a 6th girl is .5*.5*.5*.5*.5*.5 = .0156 or about 1.6%.
- We'll need the exact probabilities from the binomial distribution to answer this, you can use excel. In excel type =BINOMDIST(5,6,0.5,FALSE). The parameters are the value of interest (5 girls), the total trials (6-one boy in there), p (.5) and the logical parameter of False means to use the Probability Mass Function (PMF) which equals the exact probability for 5 out of 6. You should get about a 9.4% chance. (Note: If you change the 5 to a 6 in this example in the excel formula, you should also get .0156, the result for the second question).