# Theoretical probability

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1# Mr. Doodle's grade distribution over the past 3 years for a course in college algebra is shown in the chart below. 

Grade Number

A 45

B 180

C 110

D 95

F 65

I 5

If Jane plans to take a college algebra course with Mr. Doodle, determine the empirical probability that she receives a B.  

2#

The theoretical probability of undesirable side effects resulting from taking Grebex is 2 in 19. If 380 people take Grebex to lower their blood pressure, how many will encounter undesirable side effects?

3#

The odds against Lounging Larry winning the horse race are 2:13. Determine the probability that Lounging Larry wins the horse race.  

4#

In a multiple-choice test, each question has five options. Students will get 10 points for each correct answer; lose 2 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your calculations for expected value. Show your work for full

5#

One thousand raffle tickets are sold for $1.00 each. One grand prize of $200 and two consolation prizes of $50 each will be awarded. Jeremy purchases one ticket. Find his expected value. Show your work for full credit. 

6#

A person spins the pointer and is awarded the amount indicated by the pointer.    ￼  It costs $6 to play the game. Determine:   

The expectation of a person who plays the game.

 

The fair price to play the game.

6#

5. Determine the odds against the spinner landing on yellow

￼

#### Solution Preview

1.

The total number of grades is 45+180+110+95+65+5 = 500.

Thus, the probability she receives a B is 180/500 = 0.36.

2.

380 * 2/19 = 40

We expect 40 to encounter undesirable side effects.

3.

Odds against of 2:13 implies that there is 13 out of 13+2 = 15 probability of winning. The probability is therefore ...

#### Solution Summary

Theoretical probability is evaluated in this solution.