Question

1..Suppose an experiment has five equally likely outcomes: E1, E2, E3, E4, E5. Assign probabilities to each outcome and show that the requirements in equations (4.3) and (4.4) are satisfied. What method did you use? 2. An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use? 3. Adecision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1) .10, P(E2) .15, P(E3) .40, and P(E4) .20. Are these probability assignments valid? Explain.

Answer 1

Answer:

1.

P(E1)=P(E2)=P(E3)=P(E4)=P(E5= )1/5

2.

P(E1)=0.4

P(E2)= 0.26

P(E3)=0.34

3.

No the probability assignments are invalid

Step-by-step explanation:

1

Total number of possible outcomes = 5

Equation (4.3)

0< P(Ei)<1

Equation (4.4)

P(E1) + P(E2) +........+P(En)=1

As the outcomes are equally likely therefore,

Probability for each outcome= P(Ei) = 1/5

2

Total number of outcomes = 50

Outcomes for event E(1)= 20

Outcomes or event E(2)= 13

Outcomes or event E(3) = 17

P(Ei)= (number of outcomes for event Ei/ Total number of outcomes)

P(E1)=20/50=0.4

P(E2)= 13/50=0.26

P(E3)=17/50=0.34

3

P(E1) .10,

P(E2) .15,

P(E3) .40,

P(E4) .20

0.1 +0.15+0.40+0.20=0.85<1

According to  equation (4.4) the probability assignments are invalid as the sum of probabilities for all outcomes must be equal to 1.