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1. Russell is 5'9'' (under 6 feet). There are 130+120+35=285 players with the height under 6 feet and 120 of them are forwards. The probability that Russell is a forward is

[tex]\dfrac{120}{285}=\dfrac{8}{19}[/tex]

2. Peter is 6'2'' (over 6 feet). There are 25+30+30=85 players with the height over 6 feet and 25 of them are guards. The probability that Peter is a guard is

[tex]\dfrac{25}{285}=\dfrac{5}{57}[/tex]

JeanaShupp JeanaShupp · Answer 2 · 2019-08-18T08:37:19+02:00

Answer: A. [tex]\dfrac{8}{19}[/tex]

B. [tex]\dfrac{5}{17}[/tex]

Step-by-step explanation:

For any event A and B , the conditional probability of having B given that A is given by :-

[tex]P(A|B)=\dfrac{\text{P(A and B)}}{\text{P(b)}}[/tex]

From the given table , the total number of players = 370

A. Number of players under 6 feet = 285

Then , the probability that a player is over 6 feet :-

[tex]\dfrac{285}{370}[/tex]

Number of players that are under 6 feet and a forward = 120

Then , the probability that under 6 feet and a forward :-

[tex]\dfrac{120}{370}[/tex]

Now, if it is given that Russell is 5'9" (under 6 feet), then the probability that he is a forward:-

[tex]\text{P(Forward}|\text{under 6 feet)}=\dfrac{\text{P(under 6 feet and forward)}}{\text{P(under 6 feet)}}\\\\\text{P(Forward}|\text{under 6 feet)}=\dfrac{\dfrac{120}{370}}{\dfrac{285}{370}}\\\\\\=\dfrac{120}{285}=\dfrac{8}{19}[/tex]

B. Number of players over 6 feet = 85

Then , the probability that a player is over 6 feet :-

[tex]\dfrac{85}{370}[/tex]

Number of players that are over 6 feet and guard = 25

Then , the probability that over 6 feet and guard :-

[tex]\dfrac{25}{370}[/tex]

Now, if it is given that Peter is 6'2" (over 6 feet), then the probability that he is a guard :-

[tex]\text{P(Guard}|\text{over 6 feet)}=\dfrac{\text{P(over 6 feet and guard)}}{\text{P(over 6 feet)}}\\\\\text{P(Guard}|\text{over 6 feet)}=\dfrac{\dfrac{25}{370}}{\dfrac{85}{370}}\\\\\\=\dfrac{25}{85}=\dfrac{5}{17}[/tex]