Rudy414 wrote:Each of the variables X, Y, and Z can only be 0 or 1. The values of the three variables are independent of one another. The probability that Z is 1 is .25. The probability that X is 1 is less than the probability that Y is 1. The probability that XY + Z is at least 1 is .55.
Select the value that shows the probability that X is 1, and the value that shows the probability that Y is 1.
Possible values of XY + Z are : 0, 1, and 2
Hence, probability that XY + Z is at least 1
= 1 - probability that XY + Z is zero
= 1 - probability that XY = 0 and Z = 0
= 1 - (probability that XY = 0)*(probability that Z = 0)
= 1 - (probability that XY = 0)*(1 - 0.25)
= 1 - (probability that XY = 0)*(0.75)
So, 1 - (probability that XY = 0)*(0.75) = 0.55
--> (probability that XY = 0)*(0.75) = 1 - 0.55 = 0.45
--> (probability that XY = 0) = 0.45/0.75 = 3/5 = 0.60
Now, (probability that XY = 1) = 1 - (probability that XY = 0) = 1 - 0.60 = 0.40
And, XY will be equal to 1 when both X and Y will be equal to 1.
So, (probability that XY = 1) = (probability that X = 1)*(probability that Y = 1)
--> (probability that X = 1)*(probability that Y = 1) = 0.40
Now, looking at the options, only viable choices are : (probability that X = 1) = 0.50 and (probability that Y = 1) = 0.80
