Jessica has a bag containing 100 jelly beans. There are 20 red, cinnamon-flavored beans; 25 yellow, lemon- flavored beans; 15 green, mint-flavored beans; 30 purple, grape- flavored beans; and 10 white, pineapple-flavored beans. Find the odds in favor of picking a fruit-flavored bean. Find the odds against picking a cinnamon or mint bean. Find the theoretical probability of each of the following events: Picking a fruit- flavored bean. Not picking a cinnamon bean.

Expert Answers

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Odds equal the ratio of the number of favorable outcomes to the number of non-favorable outcomes. Notice the difference between odds and probability, which is the ratio of the number of favorable outcomes to the total number of outcomes.

The are 65 fruit-flavored beans all together: 25 lemon, 30 grape  and 10 pineapple. There are 35 beans that are not fruit-flavored. So the

odds of picking a fruit-flavored jelly bean is 65/35 = 13/7.

To find odds against picking a cinnamon or mint bean, consider which outcomes would be "favorable". You DON'T want to pick either a cinnamon or a mint, so anything else would be favorable. All other jelly beans are fruit-flavored, so the odds against picking either cinnamon or a mint are the same as the odds of picking a fruit-flavored bean: 13/7.

Odds against picking a cinnamon or mint bean is 13/7.

Theoretical probability of picking a fruit-flavored bean is the number of fruit-flavored beans divided by the total number of beans: 65/100 = 65%.

Theoretical probability of not picking a cinnamon bean is the number of all other beans (100 - 20 = 80) divided by the total number of beans:

80/100 = 80%.

The probability of not picking a cinnamon bean is 80%.

 

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