Consider an experiment in which you randomly select a real number between 0 and
ID: 3172125 • Letter: C
Question
Consider an experiment in which you randomly select a real number between 0 and 1. The sample space for the experiment is:S={x|0<=x<=1}.
Consider the following two events:
X: “the number selected is below 0.6”
Y: “the number selected is between 0.4 and 0.9”. Compute the following:
(a) The probability that X and Y happen at the same time.
(b) The probability that X happens but Y doesn’t.
(c) The probability that X doesn’t happen but Y does.
(d) The probability that neither X nor Y happens.
(e) The probability that X happens given that Y has happened.
Explanation / Answer
P(X) = 0.6/1 = 0.6
P(Y) = (0.9-0.4)/1 = 0.5
a)probability that X and Y happen at the same time. = P(X<0.6 and 0.4<X<0.9) = P(0.4<X<0.6) = 0.2/1 = 0.2
b) probability that X happens but Y doesn’t. = P(X)-Probability that X and Y happen at the same time. = 0.6-0.2 = 0.4
c)probability that X doesn’t happen but Y does = P(Y) -Probability that X and Y happen at the same time
= 0.5-0.2 = 0.4
d)probability that neither X nor Y happens = P(X>0.9) = 0.1/1= 0.1
e)probability that X happens given that Y has happened = P(X/Y) = P(X and Y)/P(Y) = 0.2/0.4 = 0.5