probability problems
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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?
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This solution exemplifies probability problems.
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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 ...
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