Question

when two basketball players are about to have a free - throw competition, they often draw names out of a hat to randomly select the order in which they shoot. what is the probability that they shoot in alphabetical order? assume each player has a different name. p(shoot free - throws in alphabetical order)= (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of orderings

The number of ways to order 2 players is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$. Here $n = 2$ and $r=2$, so $P(2,2)=\frac{2!}{(2 - 2)!}=\frac{2!}{0!}=2! = 2\times1=2$. The two possible orderings of the two - player names are (Player 1 first, Player 2 second) and (Player 2 first, Player 1 second).

Step2: Determine number of favorable orderings

There is only 1 way for the players' names to be in alphabetical order.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{1}{2}$.

Answer:

$\frac{1}{2}$