A sample space S consists of five simple events with these p

A sample space S consists of five simple events with these probabilities.

(b) Find the probabilities for these two events. (Enter your answers to two decimal places.)

(c) List the simple events that are either in event A or event B or both.


(d) List the simple events that are in both event A and event B.

Solution

b)

All probabilities should add up to 1, so

0.2 + 0.2 + 0.30 + P(E4) + P(E5) = 1

0.2 + 0.2 + 0.30 + 2P(E5) + P(E5) = 1

0.2 + 0.2 + 0.30 + 3P(E5)= 1

3P(E5)= 0.3

P(E5) = 0.1

Thus,

P(E4) = 2*0.1 = 0.2

Hence,

P(A) = 0.2 + 0.30 + 0.2 = 0.70 [ANSWER]

Meanwhile,

P(B) = 0.2 + 0.30 = 0.50 [ANSWER]

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c)

For A U B, the simples events are

{E1, E2, E3, E4} [ANSWER]

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d)

The event present in both A and B is

{E3} [ANSWER]