The probability that Coach Bennet will select three juniors is 5.5%.
The probability that Coach Bennet will select three juniors is less than the probability that the coach will select three seniors.
Total number of players = 14
Number of junior players = 6
Number of senior players = 8
Coach Bennet will select only three players from 14 players.
We need to find the probability of selecting only three players either juniors or seniors.
What are probability and combination?
Probability of an event = Number of required outcomes / Total number of outcomes.
The combination is given by:
[tex]^nC_r = \frac{n!}{r! ~(n-r)!}[/tex]
Let P(J) = Probability of selecting 3 junior players.
Since we have to select 3 players from 6 junior players,
Number of possible outcomes:
[tex]^6C_3[/tex] = 6! / 3! 3! = (6x5x4) / 3x2 = 20
Total number of outcomes:
[tex]^{14}C_3[/tex] = 14! / 3! 11! = (14x13x12) / 3x2 = 14x13x2 = 364.
P(J) = [tex]\frac{^6C_3}{^{14}C_3}[/tex]
= 20 / 364
= 0.0549
Since we need to find in % we will multiply 100.
= 0.0549 x 100
= 5.49 %
= 5.5 %
Let P(S) = Probability that the coach will select three seniors.
Since we have 8 senior players,
Number of possible outcomes = [tex]^8C_3[/tex] = 8! / 3! 5! = (8x7x6) / 3x2 = 56
Total number of outcomes = [tex]^{14}C_3[/tex] = 364
P(S) = [tex]\frac{^8C_3}{^{14}C_3}[/tex]
= 56 / 364
= 0.1538 x 100
= 15.38 %
= 15.4 %
We see that the probability that Coach Bennet will select three juniors is 5.5%.
The probability that Coach Bennet will select three juniors is less than the probability that the coach will select three seniors.
i.e P(J) < P(S)
Learn more about probability here:
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