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# Probability Calculations: Bob's Umbrella

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According to Bob, the payoffs of the several outcomes are as follows:

a. If it is sunny and he is not carrying and umbrella, 10

b. If it is sunny and he is carrying an umbrella, 8

c. If it is rainy and he is not carrying an umbrella, 2

d. If it is rainy and he is carrying an umbrella, 6

Draw the game matrix of this one-person game (vs. Nature). What should the probability of rain (P) be for Bob to take an umbrella with him?

https://brainmass.com/math/probability/probability-calculations-bobs-umbrella-594501

#### Solution Preview

Payoff matrix: Bob vs. Nature
(Numbers show Bob's payoff) Nature's strategy
Sunny Rain
Bob's strategy Umbrella 8 6
No umbrella 10 2

Let Pr = the probability of ...

#### Solution Summary

This solution shows how to use game theory to determine whether Bob should take his umbrella with him. Detailed calculations and a complete payoff matrix are given.

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