00:01
Hello student, in the given question, in part a, we have to calculate the probability that exactly 3 employees would lay off their boss.
00:27
So here we use the binomial distribution formula as probability of x equals to k which is equals to n c k multiplied by p to the power k into 1 minus p to the power n minus k.
00:49
So here n is equals to 10, k is equals to 3 which is the number of employee who would lay off their boss, p is equals to 0 .27.
01:01
So substituting this value, we get probability of x is equals to 3, x is equals to 3 which is equals to 10 c 3 multiplied by 0 .27 to the power 3 multiplied by 1 minus 0 .27 to the power 10 minus 3 which is equals to 0 .2317.
01:33
So therefore, the probability of, the probability that exactly 3 employee would lay off their boss is 0 .2317.
02:16
Now in part b, we have to find out the probability that 3 or fewer employee would lay off their boss, 3 or fewer employee, employees would lay off their bosses, their bosses.
02:47
So here we can use the cumulative binomial distribution as probability of x is less than or equals to 3 which is equals to summation of p x equals to k for k is equals to 0, 1, 2, 3.
03:09
So using binomial probability formula from part a, we can calculate each term as probability of x equals to 0 which is equals to 10 c 0 multiplied by 0 .27 to the power 0 multiplied by 1 minus 27, 1 minus 0 .27, 1 minus 0 .27 to the power 10 minus 0 which is equals to 0 .000002.
03:46
Similarly, for probability of x equals to 1 which gives the value as 0 .0003 or probability of x is equals to 2, probability of x equals to 2, we get 0 .0063 or probability of x equals to 3, we get 0 .2317...