Question

A group of students gather at Raquel's house to do a statistical assignment. In this group there are 10 women and 8 men. Of the women 5 study Management and the rest Accounting, while of the men only one studies Management and the rest Accounting.

a. If the first to arrive at the house are three girls, what is the probability that they will study the same?

b. If any three of them make the assignment, what is the probability that they will study the same thing?

c. If two are randomly selected from this set of friends and the random variable X is defined: number of friends who study Accounting between the two chosen, find the expected value and the standard deviation of X

Answer 1

a)

Probability of girls managent = 5/10 = 1/2

Probability of girls accounting= 5/10 = 1/2

probability that they will study the same = 1/2*1/2*1/2 +1/2*1/2*1/2

=1/4

= 0.25

b)

Management probability = 6/18 = 1/3

Accounting probability = 12/18 = 2/3

probability that they will study the same thing = 1/3*1/3*1/3+2/3*2/3*2/3

=0.3333

c)

X	P(X)	X*P(X)	X² * P(X)
0	0.11	0.000	0.000
1	0.44	0.444	0.444
2	0.44	0.889	1.778

mean = E[X] = Σx*P(X) =            1.3333
          
E [ X² ] = ΣX² * P(X) =            2.2222
          
variance = E[ X² ] - (E[ X ])² =            0.4444
          
std dev = √(variance) =            0.6667

Thanks in advance!

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