Question

1. Ms. Elliot invites 10 relatives to a party: her mother, 3 aunts, 2 uncles, 2 sisters, 1 male cousin, and 1 female cousin. If the chances of anyone guest arriving first are equally likely, find the probabilities that the given guests will arrive first.

a). A sister or an aunt

b). A sister or a cousin

c). A sister or her mother

d). An aunt or a cousin

e). A male or an uncle

f). A female or a cousin

2. There is 20% chance of Rain tomorrow. Therefore, the probability that it will not rain is:

(Apply Complement Rule)

Answer 1

a) P(S U A) = P(S) + P (A) - P(S intersection A)

P(S intersection A) is 0 because the person cannot be sister and aunt to Elliott at the same time

Hence required probability is 3/10 +2/10 = 0.5

b) here also the intersection part Is 0 because a person can't be sister and a cousin to Elliott at the same time.

P(S U C) = P(S) + P(C)

= 2/10+2/10= 0.4

C) P( S U M) = P(S)+ P(M) = 2/10+1/10= 0.3

D)P(A U C) = P(A)+P(C) = 3/10+2/10 = 0.5

E)P(U U MALE) = P(U)+P(MALE)-P(U INTERSECTION MALE)

here the intersection part is not 0 because Uncle is male and every male cannot be uncle

P(U) = 2/10

P(male) = 3/10

P(U intersection male) = 2/10

Hence required probability is 2/10+3/10-2/10= 0.3

F)P(F) = 7/10

P(C) = 2/10

P(F INTERSECTION C) = 1/10

hence required probability is 7/10+2/10-1/10 = 0.8

2) answer is 1-0.2 = 0.8