Applied math Urn I contains four red balls and one while bal

Urn I contains four red balls and one while ball; Urn II contains one red ball and four white balls. An um is chosen at random and then two balls are drawn without replacement from The chosen um. Let X be The number of red balls drawn. Construct a sample space for this random experiment whose outcomes specify which um is chosen, The color of (he first ball drawn, and (he color of The second ball drawn Construct a table showing The value of X foe each possible outcome. Six men and five women apply for a job at Alpha. Inc. Three of The applicants axe selected for interviews. Let X denote The number of women in The interview pool. What are The possible values of The random variable X? Obtain The number of interview pools corresponding to each possible value of X; that is. for each possible value x of X. find The number of ways that event (X = x) can occur. Describe The event {X le 1} in words and find The number of ways in which it can occur

Solution

Data from the problem is the following:

Urn I: 4 red balls, 1 white ball

Urn 2: 1 red ball, 4 white ball

In this experiment, an urn is chosen at random and two balls are drawn without replacement and X denotes the number of red balls.

a) The sample space would be the following: {(Urn 1, Red, Red), (Urn 1, Red, White), (Urn 1, White, Red),(Urn 2, Red, White), (Urn 2, White, Red), (Urn 2, White, White)}.

b)

Sample Element	Value of X
(Urn 1, Red, Red)	2
(Urn 1, Red, White)	1
(Urn 1, White, Red),	1
(Urn 2, Red, White)	1
(Urn 2, White, Red)	1
(Urn 2, White, White)	0