SOLUTION: Kristina Karganova invites 15 relatives to a party: her mother, 2 aunts, 3uncles, 4brothers, 1 male cousin, and 4 female cousins. If the chances of any one gues
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Question 1201514: Kristina Karganova invites 15 relatives to a party: her mother, 2 aunts, 3uncles, 4brothers, 1 male cousin, and 4 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
(b) A brother or a cousin
(c) A brother or her mother Answer by math_tutor2020(3817) (Show Source):
7/15 = 0.46667 approximately
3/5 = 0.6 exactly
1/3 = 0.3333 approximately
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Explanation for part (a)
event space = set of outcomes we want to happen
event space = a brother or an uncle showing up first
sample space = set of all possible outcomes
sample space = set of the 15 relatives
There are 4 brothers and 3 uncles
This gives 4+3 = 7 choices for the event space out of 15 possible relatives in the sample space.
Divide the two items to get 7/15.
It cannot be reduced further because 7 and 15 have no factors in common (other than 1).
I'll leave it in fraction form.
If you want a decimal, then 7/15 = 0.46667 approximately.
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Explanation for part (b)
4 brothers + 1 male cousin + 4 female cousins = 9 people we want to show up out of 15 total
That leads to 9/15
It can be reduced because 9 and 15 share the GCF 3.
9/15 = (3*3)/(3*5) = 3/5
Decimal form is 3/5 = 0.6 exactly
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Explanation for part (c)
4 brothers + 1 mother = 5 people out of 15 total
5/15 = (1*5)/(3*5) = 1/3
1/3 = 0.3333 approximately
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