You reach in a jelly bean bag and grab one bean. If the bag contains 30 red, 25
ID: 3176850 • Letter: Y
Question
You reach in a jelly bean bag and grab one bean. If the bag contains 30 red, 25 orange, 15 pink, 10 green, and 5 black beans. What is the probability that you will get a black bean or a red bean? Using the jelly bean distribution from problem l, what is the probability of selecting 5 beans, the first three of which are red and the next two of which are orange? Suppose there are two full bowls of cookies. Bowl l has 10 chocolate chip and 30 plain cookies, while bowl #2 has 20 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies. The cookie turns out to be a plain one. How probable is it that Fred picked it out of Bowl #1? In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order. One can make a box trifecta bet by specifying which three horses will come in first, second, and third, without specifying the order. In an eight-horse field, how many different ways can one make a trifecta bet? In an eight-horse field, how many different ways can one make a box trifecta bet?Explanation / Answer
Solution:-
1) The probability that we will get a black or red bean = 0.41176.
Number of red beans = 30
Number of black beans = 5
Number of orange beans = 25
Number of pink beans = 15
Number of green beans = 10
Total number of beans = 30 + 5 + 25 +15 + 10 = 85
The probability that we will get a black or red bean = 35/85 = 0.41176
2) The probability of selecting 5 red beans, first three are red beans and next two are oranges = 0.03713.
Number of red beans = 30
Number of orange beans = 25
Total number of beans = 30 + 5 + 25 +15 + 10 = 85
Total number of ways of selecting 5 beans = 85C5 = 32,801,517
Number of ways of selceting 5 red beans, first three are red beans and next two are oranges = 30C3 × 25C2 = 4060 × 300 = 1,218,000
The probability of selecting 5 red beans, first three are red beans and next two are oranges = 1,218,000/32,801,517 = 0.03713
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