5) Last thanksgiving, my 11-year old niece introduced me to Beanboozled - a game

Question

5) Last thanksgiving, my 11-year old niece introduced me to Beanboozled - a game in which players must draw jelly beans at random from a large container, and then eat them. The catch is that the beans come in two forms. For example, some orange beans taste like peach, others taste like barf. You can’t tell them apart until you eat them. Suppose there 3 barf-flavored beans for every 7 peach-flavored beans. If you draw and eat 2 beans, what is the probability that you will not enjoy the experience? *Assume that the jar is very large (i.e., you are pretty much sampling with replacement). I’m also assuming you do not enjoy barf-flavored jelly beans.

a) 0.51 b) 0.67 c) 0.49 d) 0.33 e) 0.41

Its says A is the answer, why

Explanation / Answer

Here as we are doing drawing with replacement, the probability of drawing a barf-flavored jelly beans and peach-flavored beans would remain same in both draws. There are 3 barf-flavored jelly beans for every 10 beans in the jar. Therefore P(barf-flavored jelly beans) = 3/10 = 0.3 and therefore, P(peach-flavored beans ) = 1 - 0.3 = 0.7

Now probability that we do not enjoy the 2 beans

= 1 - Probability that we enjoy both the beans

= 1 - Probability that both beans are peach-flavored beans

= 1 - 0.7*0.7

= 1 - 0.72

= 1 - 0.49

= 0.51

Therefore A) 0.51 is the required probability here.

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