Binomial and experimental probability

Question

Reece and Kala are playing a game with a die. As Reece rolls the die, Kala notices that it seems to land on the number 6 a lot. She notes that for 5 out of 10 rolls of the die, the die comes up as a 6.


The binomial probability of rolling five 6s out of ten throws is approximately _____. The experimental probability of rolling a 6 is _____.

Answer 1

The binomial distribution models the probability of an event happening x times out of n trials, if it has a probability of p occurring in each trial.

P(x) = _nC_x p^x (1-p)^n-x

 

Assuming a fair six-sided die, the probability of rolling a 6 should be p=1/6. In n=10 rolls, you're looking for x=5 successes. _nC_x = x! / (n! (n-x)!) is the standard combination counting function. Most scientific calculators should be able to calculate this for you.

 

The experimental probability is the probability determined by the experimental results. Out of 10 actual trials, a 6 was rolled 5 times, so the experiment determined a probability of 5/10 = 0.5.