finite math problem probability?

Question

nvolving the selection of two students from a committee of students. Assume that the committee is made up of 2 males and 5 females. Two are selected at random, and a random variable X is defined to be the number of males selected.

How many different values are possible for the random variable X?

it is 3

PART 2:

Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.

Value of XProbability
0
1
2

i have no idea how to find prob of the values of x help please

Answer 1

First, you need the number of ways to choose 2 students from 5. For this, you use the binomial coefficient,

C(n,k) = n! / [k!(n-k)!]

which is the number of ways to choose k objects from a set of n.

In this case, you have C(5,2) = 5!/[3!2!] = 10.

Of those 10 ways of choosing the two students, how many of those do not involve any males? That is equal to the number of ways to choose two females from the set of 3, which is C(3,2) = 3!/[2!1!] = 3. So, for X = 0, the probability is 3/10.

How many ways involve 2 males? Just one, since there are only 2 males available. So, for X=2, the probability is 1/10.

The probabilities must sum to 1, so that will tell you the probability for X=1.

Answer 2

You're selecting 2 people. For the first selection, the probability of selecting a male is 2/7 and the probability of selecting a female is 5/7.

X=0 means no males selected, so the probability of X=0 is the probability of selecting a female both times:

p(x=0) = p(female out of 7-person pool) * p(female out of 6 person pool) = (5/7)*(4/6) = 20/42 = 10/21

X=1 means 1 male selected.

p(x=1) = p(male from 7-person pool)*p(female from 6-person pool) + p(female from 7-person pool)*p(male from 6-person pool) = (2/7)*(5/6) + (5/7)*(2/6) = 10/42 + 10/42 = 10/21

X=2 means a male was selected both times

p(x=2) = p(male from 7-person pool)*p(male from 6-person pool) = (2/7)*(1/6) = 2/42 = 1/21

Answer 3

Part 1.
There are 2 females.
So the selected will have 0 man, 1 man or 2 men. x = (0,1,2).
Part 2.
0 is the probability that all chosen are female
1 is the probability that 1 female only is chosen
2 is the probability that 0 female are chosen