Question

PLEASE SHOW YOUR WORK

. Suppose you randomly draw one slip of paper from a bowl. Each slip of paper is identical in shape and consistency. Each slip of paper has a dollar amount you win when you select it. In the bowl, there are 12 papers worth $0, 9 papers worth $1, 5 papers worth $5, 3 papers worth $10 and 1 paper worth $100. With a random variable defined by the amount you win each time you play, build a probability distribution. [Leave all probabilities as fully reduced fractions.]

Answer 1

In the bowl,

there are 12 papers worth $0.

there are 9 papers worth $1.

there are 5 papers worth $5.

there are 3 papers worth $10.

there is 1 paper worth $100.

So, in total, there are 12+9+5+3+1, ie. 30 papers.

Now, I draw one paper randomly, and can win the amount that the paper is worth of.

Now,

probability of drawing $0 worth paper is 12/30, ie. 2/5.

probability of drawing $1 worth paper is 9/30, ie. 3/10.

probability of drawing $5 worth paper is 5/30, ie. 1/6.

probability of drawing $10 worth paper is 3/30, ie. 1/10.

probability of drawing $100 worth paper is 1/30.

So, if X be the amount that I win on one play, then X has the probability distribution.

X takes value 0 with chance 2/5.

X takes value 1 with chance 3/10.

X takes value 5 with chance 1/6.

X takes value 10 with chance 1/10.

X takes value 100 with chance 1/30.