Probability rules worksheet NAME:_____________________
1. If P(A) = 0.65 and P(B) = 0.32 and P(A∩B) = 0.27, find the following:
a. P(A U B) = 0.65 + 0.32 – 0.27 = 0.70
b. P(B|A) =
0.27 0.4154
0.65
c. Are A and B disjoint events? Why or why not?
No. P(A∩B) = 0.27 ≠ 0
d. Are A and B independent events? Why or why not?
No. P(B|A) = 0.4154 ≠ P(B) = 0.32
2. If P(G) = 0.42, P(M) = 0.33 and G and M are independent, what’s the probability of G and M?
P(G∩M) = (0.42)(0.33) = 0.1386
3. If P(W) = 0.6 and P(J) = 0.34 and P(J|W) = 0.2, find the following:
a. P(W and J) = P(W ∩ J) = P(W)∙P(J|W) = (0.6)(0.2) = 0.12
b. P(W or J) = P(W U J) = 0.6 + 0.34 – 0.12 = 0.82
4. If P(Y) = 0.45 and P(L) = 0.60 and P(Y U L) = 0.78, find the following:
a. P(Y ∩ L) = 0.78 – 0.45 – 0.60 = 0.27
b. P(L|Y) =
P(L Y) 0.27 0.60
P(Y) 0.45
c. Are Y and L disjoint events? Why or why not?
No. P(Y ∩ L) = 0.27 ≠ 0
d. Are Y and L independent events? Why or why not?
Yes. P(L|Y) = 0.60 = P(L) = 0.60
5. If P(D) = 0.32, P(R) = 0.13 and D and R are disjoint, what is the probability of D or R?
P(D U R) = 0.32 + 0.13 = 0.45
6. If P(T) = 0.51 and P(B) = 0.28 and P(B|T) = 0.18, find the following:
a. P(T and B) = P(T)∙P(B|T) = (0.51)(0.18) = 0.0918
b. P(T or B) = 0.51 + 0.28 – 0.0918 = 0.6982
