Answer:
a) 0.20
b) 0.45
c) 0.65
d) Yes
e) Yes
f) Z = X + Y (except when X = 1 and Y = 1)
This is because the successes of X and Y are mutually exclusive events but their failures aren't. X and Y cannot both be 1.
Step-by-step explanation:
Probability of a red set = 20% = 0.20
Probability of a white set = 45% = 0.45
Probability of a blue set = 35% = 0.35
Probability of the single set being a red or white set = 20% + 45% = 65% = 0.65
P(X=1) = 0.20, P(X=0) = 1 - 0.2 = 0.80
P(Y=1) = 0.45, P(Y=0) = 1 - 0.45 = 0.55
P(Z=1) = 0.65, P(Z=0) = 1 - 0.65 = 0.35
a) pX = P(X=1) = 0.20
b) pY = P(Y=1) = 0.45
c) pZ = P(Z=1) = 0.65
d) Since only one order is being considered at a time, it isn't possible to order red & white set in a single set, hence, both X and Y cannot both be successes (equal to 1) at the same time. But they can both be failures (both equal to 0) if a blue set is ordered. The successes of X and Y are mutually exclusive events but their failures aren't
e) Is pZ = pX + pY
pX = 0.2, pY = 0.45, pZ = 0.65
Hence, this statement is correct!
f) Z = X + Y
Let's check all the probabilities
when X = 1 and Y = 1, Z = 1
1 ≠ 1 + 1
when X = 0 and Y = 1, Z = 1
1 = 0 + 1
when X = 1 and Y = 0, Z = 1
1 = 1 + 0
when X = 0 and Y = 0, Z = 0
0 = 0 + 0
Hence, Z = X + Y (except when X = 1 and Y = 1)
This is because the success of X and Y are mutually exclusive events but their failures aren't.
= h