Question

A young engineering student tries to decide what she will do on Sunday evening. She has three options; going to cinema (C), going to bowling saloon (B), going to a restaurant (R). She may choose C option with probability 0.4, B option with probability 0.2 and R option with probability 0.4. If she chooses cinema option, she may go to three movies; a thriller (CT), a cartoon (CC) and romantic comedy (CR). Conditional probabilities associated with these three movie options are 0.6, 0.35 and 0.05. If she chooses to go to bowling saloon, she has two options; Rocker House (BR) with probability 0.7 and Empire Bowling (BE) with probability 0.3. Restaurant options are Chinese (RC) with probability 0.1, Burger House (RB) with probability 0.2 and Urfa Kebap (RU) with probability 0.7. a) (16 Points) Draw the decision trees diagram for these options.A young industrial engineering student tries to decide what she will do on Sunday evening. She has three options; going to cinema (C), going to bowling saloon (B), going to a restaurant (R). She may choose C option with probability 0.4, B option with probability 0.2 and R option with probability 0.4. If she chooses cinema option, she may go to three movies; a thriller (CT), a cartoon (CC) and romantic comedy (CR). Conditional probabilities associated with these three movie options are 0.6, 0.35 and 0.05. If she chooses to go to bowling saloon, she has two options; Rocker House (BR) with probability 0.7 and Empire Bowling (BE) with probability 0.3. Restaurant options are Chinese (RC) with probability 0.1, Burger House (RB) with probability 0.2 and Kebap (RK) with probability 0.7

. a) Draw the decision trees diagram for these options.

b) Compute the probabilities for whole options

Answer 1

Solution:-

Given that

A young engineering student tries to decide what she will do on Sunday evening. She has three options; going to cinema (C), going to bowling saloon (B), going to a restaurant (R). She may choose C option with probability 0.4, B option with probability 0.2 and R option with probability 0.4. If she chooses cinema option, she may go to three movies; a thriller (CT), a cartoon (CC) and romantic comedy (CR). Conditional probabilities associated with these three movie options are 0.6, 0.35 and 0.05. If she chooses to go to bowling saloon, she has two options; Rocker House (BR) with probability 0.7 and Empire Bowling (BE) with probability 0.3. Restaurant options are Chinese (RC) with probability 0.1, Burger House (RB) with probability 0.2 and Urfa Kebap (RU) with probability 0.7

. a) Draw the decision trees diagram for these options.

The decision tree diagram can be drawn using given probabilities for different options as below.

b) Compute the probabilities for whole options

Using the above drawn decision tree we can calculate probabilities of different options as below.

P(CT) = 0.6 x 0.4 = 0.24

P(CC) = 0.35 x 0.4 = 0.14

P(CR) = 0.05 x 0.4 = 0.02

P(BR) = 0.7 x 0.2 = 0.14

P(BE) = 0.3 x 0.2 = 0.06

P(RC) = 0.1 x 0.4 = 0.04

P(RB) = 0.2 x 0.4 = 0.08

P(RU) = 0.7 x 0.4 = 0.28

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