Rules for Probability 4.5

P(E)+P(F)-P(E or F)

For any event E in sample space S, P(E U F)=

0 and 1

For any event E in sample space S, P(E) is between or equal to

1

For any event E in sample space S, P(S)=

P(E)+P(F)

For mutually exclusive events, P(E U F)=

1- P(E)

For mutually exclusive events, P(E to the c)=

1-P(E to the c)

For mutually exclusive events, P(E)=

0.5

If E and F are two disjoint events in S with P(E) = 0.19 and P(F) = 0.31. P((E ∪ F)C)=

0

If E and F are two disjoint events in S with P(E) = 0.19 and P(F) = 0.31. P(E ∩ F)=

0.5

If E and F are two disjoint events in S with P(E) = 0.19 and P(F) = 0.31. P(E ∪ F)=

0.81

If E and F are two disjoint events in S with P(E) = 0.19 and P(F) = 0.31. P(EC)=

1

If E and F are two disjoint events in S with P(E) = 0.19 and P(F) = 0.31. xP((E ∩ F)C)=

P(E)= a over a + b

If the odds are given as a over b

4/13

If the odds for a successful marriage are 4:9, what is the probability of a successful marriage?

5/13

If the odds for a successful marriage are 5:8, what is the probability of a successful marriage?

0.32

Let E and F be two events in S with P(E) = 0.47, P(F) = 0.52, and P(E ∪ F) = 0.67. P(E ∩ F)=

0.15

Let E and F be two events in S with P(E) = 0.47, P(F) = 0.52, and P(E ∪ F) = 0.67.P(E ∩ FC)=

0.72

Let E, F and G be three events in S with P(E) = 0.57, P(F) = 0.55, P(G) = 0.64, P(E ∩ F) = 0.36, P(E ∩ G) = 0.43, P(F ∩ G) = 0.38, and P(E ∩ F ∩ G) = 0.28. P(EC ∪ FC ∪ GC) =

0.43

Let S = {a, b, c, d, e, f} with P(a) = 0.26, P(b) = 0.14, P(c) = 0.17, P(d) = 0.19, P(e) = 0.11, and P(f) = 0.13. Let E = {d, e, f} and F = {a, b, d, f}. Find P(E) and P(F). P(E)=

0.72

Let S = {a, b, c, d, e, f} with P(a) = 0.26, P(b) = 0.14, P(c) = 0.17, P(d) = 0.19, P(e) = 0.11, and P(f) = 0.13. Let E = {d, e, f} and F = {a, b, d, f}. Find P(E) and P(F). P(F)=

0.59

Let S = {a, b, c, d, e, f} with P(b) = 0.12, P(c) = 0.2, P(d) = 0.15, P(e) = 0.14, and P(f) = 0.21. Let E = {a, c, f} and F = {b, c, e, f}. Find P(a), P(E), and P(F). P(E)=

0.67

Let S = {a, b, c, d, e, f} with P(b) = 0.12, P(c) = 0.2, P(d) = 0.15, P(e) = 0.14, and P(f) = 0.21. Let E = {a, c, f} and F = {b, c, e, f}. Find P(a), P(E), and P(F). P(F)=

0.18

Let S = {a, b, c, d, e, f} with P(b) = 0.12, P(c) = 0.2, P(d) = 0.15, P(e) = 0.14, and P(f) = 0.21. Let E = {a, c, f} and F = {b, c, e, f}. Find P(a), P(E), and P(F). P(a)=

0.51

Let S = {a, b, c, d, e, f} with P(b) = 0.24, P(c) = 0.1, P(d) = 0.13, P(e) = 0.12, and P(f) = 0.22. Let E = {a, c, f} and F = {c, d, e, f}. P(E)=

0.57

Let S = {a, b, c, d, e, f} with P(b) = 0.24, P(c) = 0.1, P(d) = 0.13, P(e) = 0.12, and P(f) = 0.22. Let E = {a, c, f} and F = {c, d, e, f}. P(F)=

0.19

Let S = {a, b, c, d, e, f} with P(b) = 0.24, P(c) = 0.1, P(d) = 0.13, P(e) = 0.12, and P(f) = 0.22. Let E = {a, c, f} and F = {c, d, e, f}. P(a)=

P(E) over P(E to the c)= P(E) over 1- P(E)

The odds in favor of an Event E are