Question

Consider the Monty Hall problem. Let’s label the door with the car behind it a and the other two doors b and c. In the game the contestant chooses a door and then Monty chooses a door, so we can label each outcome as ‘contestant followed by Monty’, for example ab means the contestant chose a and Monty chose b.

(a) Make a 3 × 3 probability table showing probabilities for all possible outcomes. (3 marks)

(b) Make a probability tree showing all possible outcomes. (3 marks)

(c) Suppose the contestant’s strategy is to switch. List all the outcomes in the event ‘the contestant wins a car’. What is the probability the contestant wins? (4 marks)

Answer 1

solution: Page 1 * According to given data consider the Monty Hall problem. Let's label the door with the car behind it a and the (a) & (b) In the is the contestants tree, the first row choice and the host's (Monty's) choice. second row is the viewed as table: contestant. a b o 0 Host b1 % o / // c Viewed as tree: // V3 1113 a a b c a

Page 2 b ) =) with this strategy the contestant wing with {bc, cb} :: The probability of winning is p{bc)*P(cd)-2 {ab, ac}, Probability = 1/2 Х Please give me thumb up.