00:01
Hello student, suppose that only 25 % of all drivers came to complete the shop at the intersection having the flashing red light in all directions.
00:11
Then given information is that e is equal to 25 % which is equal to 0 .25.
00:21
And when the no other cars are visible.
00:24
What is the probability that of the 20 randomly chosen drivers coming to the intersection then sample size n equals to 20 and we have to find the number of probabilities here.
00:38
The first priority is at most 6 came to the complete stop then x is less than or equals to 6 then exactly 6 will come to the complete the stop then probability of x equals to 6 next priority at least 6 will came to the complete the stop then x is greater than or equals to 6 and the last one is how many of the next 20 drivers do you expect to come to the complete the stop then expectation of x.
01:11
We have to calculate these all quantities one by one.
01:15
First we have to find the distribution of the x.
01:19
Let x be the random variable and it follows here a binomial distribution.
01:23
Why binomial distribution? because the number of tries are fixed and the probability of success is again fixed here which is 0 .25 and all the random variables are independently distributed.
01:35
Then the emf of binomial distribution is given as p of x equals to x is equals to ncx p raise to x 1 minus p raise to n minus x and x is our random variable.
02:03
It takes values from 0 1 2 up to n which is equals to 0 otherwise.
02:09
Then first probability which we have to find is probability of x greater than or equals to 6 sorry less than or equals to 6 at most and less than or equals to 6.
02:22
The value of n is 20 then the possible values of x here are starting with the 0 0 1 2 3 4 5 and 6 which is equal to and we know that in our binomial distribution all the variables are independently distributed.
02:45
Then take the probabilities of the all individual random variables up to the point 6 and by using the pmf function we can find the probabilities of the individual functions.
03:02
Then first x equals to 0 then n equals to 20 x equals to 0 probability of success is 0 .25 raise to x which is a 0 1 minus 0 .25 raise to n minus x n is 20 minus x 0 and again we know that nc0 is always 1 then 20c0 is 1 anything raise to 0 is again 1 into 1 minus 2 25 0 .25 raise to 20 and after simplification we get this value at 0 .003.
03:41
Therefore probability of x equals to 0 we get this value at 0 .003.
03:47
Similarly we can calculate the probability of x equals to 1 and we get this value at 0 .021...