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In: Statistics and Probability

You get bit by a zombie. You have 3 antidote pills but they have been mixed...

You get bit by a zombie. You have 3 antidote pills but they have been mixed in a bottle with 4 aspirin and 5 heart pills. If you take more than 4 heart pills, then you will die. Therefore, you choose 4 pills at random. What is your probability of survival? That is, what is the probability that you randomly choose at least one antidote pill?

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Expert Solution

solution:

Number of antidote pills in the bottle = 3

Number of aspirin pills in the bottle = 4

Number of heart pills in the bottle = 5

Total number of pills in the bottle = 3+4+5 =12

Number of non-antidote pills in the bottle = Number of aspirin pills in the bottle+Number of heart pills in the bottle=4+5=9

Number of pills chosen at random = 4

Probability that you randomly choose at least one antidote pill = 1 - Probability that you randomly choose all non-antidote(aspirin or heart) pills

Probability that you randomly choose all non-antidote(aspirin or heart) pills

=Number of ways of selecting 4 non-antidote(aspirin or heart) pills from 9 non-antidote(aspirin or heart) pills / Number of ways of selecting 4 pills from 12 pills

Probability that you randomly choose at least one antidote pill = 1 - Probability that you randomly choose all non-antidote(aspirin or heart) pills = 1 - 14/55 = 41/55 = 0.745454545
Probability that you randomly choose at least one antidote pill = 41/55 = 0.745454545

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orchestra answered 1 year ago
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