Question

A person bets his remaining savings on a horse race based on the large payoff if his horse wins. Which of the following decision-making criteria does this typify?

Choose one answer.

	a. Maximax
	b. Maximum expected payoff
	c. Minimax
	d. Minimax regret

Jake woke up late in the morning on the day that he has to go to school to take an important test. He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice. If Jake, in fact, gets to the test on time, what is the probability that he took the bus?

Choose one answer.

	a. 0.333
	b. 0.5714
	c. 0.667
	d. 0.4286

Answer 1

Question 1) The given type of decision making is known as Maximax. Maximax is the strategy in game theory where the player facing uncertainty chooses the strategy that gives the player maximum payoff. So option a is the correct answer.

Question 2) It is given that the probability that the shuttle bus is late = 0.2

Probability that the motorcycle breaks down = 0.4.

Probability of choosing to go by bus = 0.5.

Probability of choosing to go by motorcycle = 0.5.

So, the probability that Jake reached the school on time = Probability of choosing bus and the bus is not late + Probability of choosing motorcycle and the motorcycle does not break down.

= 0.5*(1-0.2) + 0.5*(1-0.4)

= 0.5*0.8 + 0.5*0.6

= 0.7

The probability that Jake chose to go by bus when it is given that reached school on time =

Probability of choosing bus and the bus is not late / Probability that Jake reached school on time

= (0.5*0.8) / 0.7

= 0.4 / 0.7

= 0.5714

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