Question

A sample space consists of five simple events, E1, E2, E3, E4, and E5. a If P(E1) = P(E2) = 0.15, P(E3) = 0.4, and P(E4) = 2P(E5), find the probabilities of E4 and E5.
b If P(E1) = 3P(E2) = 0.3, find the probabilities of the remaining simple events if you know that the remaining simple events are equally probable.

Answer 1

Answer:

Step-by-step explanation:

Given that

A sample space consists of five simple events, E1, E2, E3, E4, and E5.

a If P(E1) = P(E2) = 0.15,

P(E3) = 0.4, and P(E4) = 2P(E5),

We know that total probability =1

i.e. sum of probabilities of All Eis would be 1

$0.15+0.15+0.4+2x+x=1$

where x = P(E5)

Solving for x we get

x=0.30

So P(E4) = 0.2 and P(E5) = 0.1

-----

b) Let P(E3) =P(E4) = P(E5) = y

then we have

total probability = $0.3+0.1+3y =1\\3y =0.6\\y = 0.2$

Probability of remain are 0.2 each.