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Using the combination formula, it is found that the integers can be chosen in 870 ways.
<h3>What is the combination formula?</h3>
is the number of different combinations of x objects from a set of n elements, given by:
The resulting sum will be even if both numbers are even(2 from a set of 30) or if both numbers are odd(also 2 from a set of 30), hence:
The integers can be chosen in 870 ways.
You can learn more about the combination formula at brainly.com/question/25821700
Answer:
a)
b)
c)
d)
e)
Step-by-step explanation:
1) 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".
2) Solution to the problem
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:
3) Part a
4) Part b
5) Part c
6) Part d
The expected value is:
7) Part e
The variance is given by: