Question

the table shows the distribution of 88 basketball players and their positions on a basketball club. each player is categorized in one position.
position point guard shooting guard small forward power forward or center frequency 26 16 11 35
if one of the 88 players is selected at random, the probability of selecting a player who is categorized as a power forward, given the player is not categorized as a shooting guard is 3/12. how many of these players are categorized as a center?

Explanation:

Step1: Calculate total number of non - power forward players

The total number of players is \(88\). The number of power forward players is \(35\). So the number of non - power forward players is \(88 - 35=53\).

Step2: Calculate the probability of selecting a non - power forward player

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (selecting a non - power forward player) is \(53\) and the total number of outcomes (selecting any player) is \(88\). So the probability \(P = \frac{53}{88}\).

Answer:

\(\frac{53}{88}\)