Question

Please answer I’ll rate brainlyest

Answer 1

Answer: A. $\dfrac{8}{19}$

B. $\dfrac{5}{17}$

Step-by-step explanation:

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

$P(A|B)=\dfrac{\text{P(A and B)}}{\text{P(b)}}$

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 :-

$\dfrac{285}{370}$

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

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

$\dfrac{120}{370}$

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

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

B. Number of players over 6 feet = 85

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

$\dfrac{85}{370}$

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

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

$\dfrac{25}{370}$

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

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

Answer 2

Answer:

1. $\dfrac{120}{285}=\dfrac{8}{19}$

2. $\dfrac{25}{285}=\dfrac{5}{57}$

Step-by-step explanation:

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

$\dfrac{120}{285}=\dfrac{8}{19}$

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

$\dfrac{25}{285}=\dfrac{5}{57}$