Question
In: Statistics and Probability
A college basket ball team has 15 players, 5 seniors, 8 juniors, and 2 sophomores. Two...
A
college basket ball team has 15 players, 5 seniors, 8 juniors, and
2 sophomores. Two players are randomly selected to serve as captain
for the next game, what’s he probability both selected are
seniors?
Solutions
Expert Solution
Answer
We have a total of 15 players, which consists of 5 seniors, 8
juniors and 2 sophomores
We need to the find the probability of selecting both captains from
seniors.
Number of ways of selecting both captain from senior is
C(5,2)*C(8,0)*C(2,0)
C stands for combination
We know that Combination(8,0) = 8!//[(8-0)!*0!] = 1
And Combination(2,0) = 2!//[(2-0)!*0!] = 1
So, Number of ways of selecting both captain from senior is
C(5,2)*C(8,0)*C(2,0), this can be written as
Number of ways of selecting both captain from senior = C(5,2)*1*1 =
5!/[(5-2)!*2!] = 10 ways
Number of ways of selecting 2 players from 15 = Combination(15,2) =
15!/[(15-2)!*2!] = 105
So, the required probability = C(5,2)/ C(15,2) = 10/105 = 0.0952 (rounded to 4 decimal places)
orchestra answered 2 years agoRelated Solutions
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DATA 3 8 2 15 2 2 0 0 4 5 2 7 0 1 5...
DATA
3
8
2
15
2
2
0
0
4
5
2
7
0
1
5
3
0
2
5
4
1
6
9
5
3
1
2
10
6
1
1
2
1
19
6
6
6
7
0
4
1
1
1
0
1
9
2
2
2
1
16
10
10
5
2
3
1
4
4
4
3
6
2
8
5
2
7
1
6
4
0
3
1
1
1
Background:
A group of...
Data: 7,-5, -8, 7, 9, 15, 0, 2, 13, 8, 6, -2, 4 (a) Mean= Mode=...
Data: 7,-5, -8, 7, 9, 15, 0, 2, 13, 8, 6, -2, 4 (a) Mean= Mode=
median= (b) Variance= Standard deviation= (c) Range=
IQR(Interquartilerange)= (d) Mid-Range= Mid-Hinge=
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