According to Alice, payoffs of several outcomes are as follows:
i) If it is sunny and she is not carrying umbrella, 10.
ii) If it is sunny and she is carrying umbrella, 8.
iii) If it is rainy and she is not carrying umbrella, 2
iv) if it is rainy and she is carrying umbrella, 6
Sketch the game matrix of one-person (vs. Nature). What must probability of rain (P) be for Alice to take an umbrella with her?