finite math question, question in description, too many characters to fit

Question

A radio station runs a promotion at an auto show with a money box with

11

​$50

​tickets,

10

​$25

​tickets, and

10

​$5

tickets. The box contains an additional

20

​"dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that exactly two

​$50

prizes and no other money winners are chosen.

The probability that exactly two

​$50

prizes and no other money winners are chosen is

Answer 1

A radio station runs a promotion at an auto show with a money box with 11 ​$50 ​tickets, 10 ​$25 ​tickets, and 10 ​$5 tickets. The box contains an additional 20 ​"dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that exactly two ​$50 prizes and no other money winners are chosen.

First let’s name some variables to make this problem easier to solve:

Y - $50 ticket

T - $25 ticket

F - $5 ticket

D - dummy ticket

Now let’s look at the money box with just the letters inside:

YYYYYYYYYYY

TTTTTTTTTT

FFFFFFFFFF

DDDDDDDDDD

DDDDDDDDDD

Since these draws are considered independent events we can multiply the probabilities together.

First we need the probability of drawing two $50 tickets out of three draws:

P(FFD)= (10/51)(9/50)(20/49) = .014

Since there are three different ways that exactly two $50 tickets can be drawn out of three draws:

FFD, FDF, DFF

We simply add these probabilities together:

.014 + .014 + .014 = .043