00:01
It's stated in the question that 9 % of the population is left -handed.
00:06
So that means it's a probability of 0 .09 for any randomly selected individual for being left -handed.
00:15
And we consider four people that are randomly selected.
00:18
And we were asked for the probabilities that certain numbers of them are left -handed.
00:23
So let's define this random variable x as the number of left -handed people in the random sample of four.
00:29
In this situation, each of the four people can be thought of as bernoulli trials with two outcomes of interest, either left -handed or not.
00:38
And since it's a random sample, their outcomes are independent.
00:42
The number of successes in a fixed number of independent bernoulli trials is a binomial random variable.
00:49
So here we can say x is a binomial based on four trials and probability of success on each trial, 0 .09.
00:59
Now the probability function for the binomial random variable is in general given by this formula.
01:19
Part a, we were asked for the probability that all of them are left -handed.
01:23
This is the probability that x is equal to 4...