3 You lost your keys in one of classrooms 1, 2, 3, or 4. You believe that they a

Question

3 You lost your keys in one of classrooms 1, 2, 3, or 4. You believe that they are in classrooms 1, 2, or 3 with probability 03 for each, or in classroom 4 with probability 0 1. You have just enough time to search three classrooms, but your friend Shannon has offered to help you look. Given your past experience, you know that Shannon has a probability 0.6 and you have a probability 0.8 of finding the keys when searching in the room that has the keys You are twice as fast as Shannon (a) What is the probability of finding the keys if you looked in classrooms 1 and 2, while Shannon searched 3, and classroom 4 remained unchecked? (b) What is the conditional probability that the keys are in room 3, given that the keys were not found after the search described in (a)? (c) Assume that the keys were not found after the search described in (a), but you have time to search one more room. Which of the four rooms would you pick? What would the probability of finding the keys be after you searched your room of choice? (d) Note that you had the option to search rooms 1, 2, and 3, while Shannon looked in 4 What would be the probability of of finding the keys under this search strategy? a

Explanation / Answer

Answer to part c)

definitely I would go and search room 4

the probability of getting key in room# 4 is 0.1

.

After I searched the room of my choice;

There are chances that I failed to find the key in room# 1 & 2

P = 0.2 *(0.3+0.3) = 0.12

There are chances that shannon failed to find key in room # 3

P = 0.4 *0.3 = 0.12

Thus there is still: 0.12 +0.12 = 0.24 chance of finding the keys

.

Answer to part d)

If the strategy is that I search rooms 1 ,2 and 3 and Shanon looks in room 4, the probability of find the key under this strategy would be

P(Me) = 0.8 *(0.3+0.3+0.3) = 0.8 * 0.9 = 0.72

P(shannon) = 0.6 * 0.1 = 0.06

Thus total probability = 0.72+0.06 = 0.78

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