Answer:
a) For this case we can use the binomial model since we assume independent events and the same probability for each trial is the same p =0.15
b)
c)
d)
And using the result from part a we got:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
Part a
For this case we can use the binomial model since we assume independent events and the same probability for each trial is the same p =0.15
Part b
For this case we want this probability:
And replacing we got:
Part c
For this case we want this probability:
And replacing we got:
Part d
For this cae we want thi probability:
And we can use the complment rule and we got:
And using the result from part a we got: