00:01
In the question, it is given that probability of success p is equal to 0 .1, sample size n is equal to 6.
00:08
Therefore, q is equal to 1 minus p, which is equal to 1 .0 .9.
00:17
Here, the random variable x follows binomial distribution with parameter np.
00:23
We know that binomial probability rule states that the probability of x success and n -minus, as x failure in an independent trial of an experiment which has a p as a probability of success in a single trial is obtained by the formula n c x p r s to x q rest to n minus x in the a part we have to obtain the probability that no one has done one time flea that is probability that x is equal to zero which is equals to 6c0 0 0 .1 1 rest to 0 into 0 .9 rest to 6 minus 0 which is equals to 6c0 0 .1 rest to 0 into 0 .9 rest to 6 which is equals to if we saw this particular quantity we'll get the value as 0 .531 therefore the answer for a part is 0 .531.
01:24
In the b part we have to obtain the probability that at least one person has done a 1 time that is probability that x is greater than or equal to 1.
01:35
Here sample size is 6, therefore this probability is equal to probability that x is equal to 1 plus probability that x is equal to 2 plus probability that x is equal to 3 plus probability of x is equal to 4 plus probability that x is equal to 5 plus probability that x is equal to 6.
02:01
We'll compute this probabilities 1 by 1.
02:04
Firstly, probability that x is equal to 1 is equal to 6c1 .1 .1 .9 rest to 6 minus 1, which is equals to 0 .3543...