# probability problems

1: The theoretical probability of undesirable side effects resulting from taking Grebex is 1 in 12. If 600 people take Grebex to lower their blood pressure, how many will encounter undesirable side effects?

2: If the odds of winning a raffle are 2:229, what is the probability of winning?

3: One thousand raffle tickets are sold for $1.00 each. One grand prize of $400 and two consolation prizes of $100 each will be awarded. Jeremy purchases one ticket. Find his expected value. Show all the work.

4: Each of the numbers 0 through 30 is written on a piece of paper and all of the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is even.

5: Which pair has equally likely outcomes? Select the two choices below which have equal probabilities of success. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Show all the work.

a. Rolling a sum of 4 on two fair six sided dice.

b. Drawing a black seven out of a standard 52 card deck given it is not a face card or an Ace.

c. Rolling a sum of 11 on two fair six sided dice.

d. Rolling a sum of 7 on two fair six sided dice.

e. Drawing a three out of a standard 52 card deck given it is not a face card or an Ace.

6: A bag contains 7 lavender marbles, 11 turquoise marbles and 5 rainbow marbles. What is the chance of drawing a turquoise marble? If a turquoise marble is drawn then placed back into the bag, and a second marble is drawn, what is the probability of drawing a rainbow marble?

#### Solution Preview

1: One of every 12 people will encounter side effects, so out of 600 people 1/12 * 600 = 50 people will encounter side effects.

2: There are 2 chances of winning out of 229+2=231 chances, so the probability of winning is 2/231.

3: The expected value is the sum of the values of the variable multiplied by their probability. We have 997 cases of winning 0 dollars, one chance of winning 400 dollars and 2 chances of winning 100 dollars. All are equally probable with the probability of 1/1000 = 0.001, so the expected value is 997*(0*0.001)+1*(400*0.001)+2*(100*0.001)=0+0.4+0.2 = 0.6 .

4: There are 16 even numbers (including 0) between 0 ...

#### Solution Summary

This solution exemplifies probability problems.