Kristina Karganova invites 15 relatives to a party: her mother, 4 aunts, 2 uncles, 4 brothers, 1 male cousin, and 3 female cousins:

Kristina Karganova invites 15 relatives to a party: her mother, 4 aunts, 2 uncles, 4 brothers, 1 male cousin, and 3 female cousins. If the chances of any one guest arriving first are equally likely, find the probabilities that the first guest to arrive is as follows.
a)A brother or an uncle
The total number of outcomes is 15 (All the 15 relatives)
The number of outcomes in the event is (no of brothers and uncles) =4+2=6.
P (brother or uncle) = P(brother)+P(uncle)=4/15+2/15=6/15
Simplify by dividing by 3, answer becomes 2/5
(b) A brother or a cousin
P(cousin)= (I male cousin+3 female cousins) =4/15
P (brother or cousin) = P(brother)+P(cousin)=4/15+4/15=8/15
Answer is 8/15
(c) A brother or her mother
P (brother or mother) =P(brother)+P(brother)=4/15+1/15=5/15
Answer is 5/15, simplifies to 1/3

Kristina Karganova invites 12 relatives to a party: her mother, 3 aunts, 2 uncles, 2 brothers, 1 male cousin, and 3 female cousins. If the chances of any one guest arriving first are equally likely, find the probabilities that the first guest to arrive is as follows.
(a) A brother or an uncle
P (brother or uncle) =P(brother)+P(uncle)=2/12+2/12=4/12, simplifies to 1/3
Answer is 1/3
(b) A brother or a cousin
P (brother or cousin) =P(brother)+P(cousin)=P(brother)+P (1 male cousin+3 female cousins)
Becomes=2/12+4/12=6/12
Simplifies to 1/2
(c) A brother or her mother
P (brother or mother) =P(brother)+P(mother)=2/12+1/12=3/12
Simplifies to 1/4

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