Question

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

P(E1) = P(E2) = 0.15
P(E3) = 0.4
P(E4) = 2P(E5)

a) Find the probabilities for simple events E4 and E5.

How do I do this?

Answer 1

let x = P(E5)

so P(E4) = 2*P(E5) = 2*x

Answer 2

for this distribution to be a true probability distribution, all of the probabilities must add to 1

P(E1) + P(E2) + .... + P(E5) = 1

Answer 3

right but how do i fugure the probability out from x?

Answer 4

P(E1) + P(E2) + P(E3) + P(E4) + P(E5) = 1

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

solve for x

Answer 5

x = 0.10?

Answer 6

once you find x, you'll know P(E5)

double x to get P(E4)

Answer 7

x = 0.10 is correct

Answer 8

Thank you Jim :)

Answer 9

np