00:01
In the a part, we have to obtain the probability that batch will be accepted.
00:06
If we observe the problem carefully, then we'll get the idea that the random variable follows binomial distribution.
00:14
We know that the binomial probability rule states that the probability of x success and n minus x failure in an independent trial of an experiment, which has a p as a probability of success in a single trial, can be obtained by the formula.
00:30
P rest to x q rest to n minus x where p plus q is equal to one and it is equal to zero otherwise the number of defectives can be zero one and two therefore the desired probability is equal to probability that x is equal to 0 plus probability that x is equal to 1 plus probability that x is equal to 2 substitute tain as a n and x as a 0 1 2 and probability of success that is p is equal to 0 .1 in this above formula to obtain the desired probability therefore x is equal to 0 tain c 0 .1 .1 rest to n x that is 0 .9 rest to 10 minus 0 plus 10 c1 .1 0 .1 rest to 1 .9 rest to 10 minus 1 plus 10c2 .1 0 .1 rest to 2 .0 .9 rest to 10 minus 2 which is equals to if we solve this above equation then we'll get the values as which is equal to 0 .928.
02:09
Therefore, the answer for a part is 0 .9 to 98.
02:14
In the b part, we have to obtain the probability that among 10 components, 5 of them are defective.
02:22
That is probability that x is equal to 5, which is nothing but 10c 5, 0 .1 rest to 5, 0 .9 rest to 10 minus 5, which is equals to 10c5 .1 rest to 5 .0 .9 rest to 5 which is equals to 0 .00148...