Question

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?

Solutions

Expert 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

orchestra answered 1 year ago
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