2.73 Avehicle arriving at an intersection can turn left, turn right, or continue

Question

2.73 Avehicle arriving at an intersection can turn left, turn right, or continue straight ahead. An experiment consists of observing the movement of one vehicle at this intersection. a List the outcomes in the sample space. b List all possible events. If the vehicle turns right at the intersection, which event(s) in part (b) has (have) occurred. d Find the probability that the vehicle turns, assuming that each outcome in part (a) is equally likely. When a patrolwoman monitors the speed of traffic using a radar gun, she may take any one of three possible actions for each car. She can let the car continue without stopping. She can stop the car and either issue a warning or issue a ticket. An experiment consists of observing the action of a patrolman after she records the speed of a car using the radar gun a List the outcomes in the sample space. b List all possible events. c If she issues a warning to the driver of a car, which event(s) in part (b) has (have) occurred d Attach probabilities to the outcomes in the sample space if the probability of the patrolman 2.74 issuing a ticket is twice that of issuing a warning and a third of that of allowing the car to continue on. Find the probability that the patrolwoman stops the car under the probabilistic model of part (d). e After a person interviews for admission to a medical school, he may be admitted, wait-listed, or denied admission. An experiment consists of observing the outcome for a person who interviews for medical school. 2.75 a b c d List the outcomes in the sample space. List all possible events. If the person is admitted, which event(s) in part (b) has (have) occurred. Attach probabilities to the outcomes in the sample space if the probability of being wait-listed is half that of being admitted and three times as many applicants are denied than are admitted.

Explanation / Answer

Since it hasn't been specified which question to answer, I will answer the first one only. More so because the rest are very similar.

2.73)

a) Possible outcomes:

L = Turn Left

R = Turn Right

S = Go Straight Ahead

----> Sample space = {L, R, S}

Sample space consists of all possible outcomes.

b) An event is simply any subset of the sample space.

There will be 23 = 8 events.

Events = {(0}, (L), (R), (S), (LR), (LS), (RS), (LRS)}

c) If the vehicle turns right at the intersection, this will correspond to the single event, E : (R)

d) Prob(vehicle turning) = Prob(vehicle turning left) + Prob(vehicle turning right)

Prob(vehicle turning) = 1/3 + 1/3 = 2/3

Ans: 2/3

Cheers!

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