00:01
It is given that the graduation rate for medical students admitted through special programs is 92 .4 percentage, that is, probability is 0 .924.
00:16
If 11 students are randomly selected from the special programs, we need to find probability that at least 10 of them graduated.
00:27
Consider x denotes graduated through special program.
00:42
That is, we need to find probability of x greater than or equal to 10.
00:48
The given situation follows binomial distribution.
00:54
This probability can be obtained by adding probability of x is equal to 10 plus probability of x is equal to 11.
01:06
The formula to find the probability of a binomial random variable is n factorial by x factorial into n minus x factorial p power x 1 minus p power n minus x here p is probability of success and n is the number of trials.
01:34
Substituting these values in the probability formula we get 11 factorial by 10 factorial into 11 minus 10 factorial 0 .9 to 4 power 10 1 minus 0 .9 to 4 power 11 minus 10 plus 11 factorial by 11 minus 10 plus 11 factorial by 11.
02:06
7 factorial into 11 minus 11 factorial 0 .924 power 11 into 1 minus 0 .924 power 11 which is equal to 0 .3792 plus 0 .41192 which is equal to 0 .3792 plus 0 .4192 which is equal to 0 .7984.
02:37
Therefore, if 11 of the students from the special programs are randomly selected, the probability that at least 10 of them graduated is 0 .7984.
02:50
Now, we need to find if 11 of the students from the special program or randomly selected, the probability that exactly 8 of them graduated, that is, probability of x is equal to 8.
03:05
Substituting the values of n and x in probability for binomial random variable, we get 11 factorial by 8 factorial into 11 minus 8 factorial 0 .924 power 8 .1 minus 0 .924 power 11 minus 8.
03:32
This is equal to 0 .0385.
03:38
Therefore, the probability that exactly 8 of them are graduated is 0 .0385...