We are told that 500 boys, including Josh and Sokka, entered a drawing for two football game tickets. We are asked to find the probability that Josh and Sokka win the tickets. To do that, we will compare the number of favorable outcomes with the number of possible outcomes.
P=Favorable outcomes/Possible outcomes
Let's first calculate the number of possible outcomes of the drawing. Since each winner of the drawing gets the same ticket for a football game, the order of choosing the winners does not matter. Therefore, we will use combinations to calculate the number of possible outcomes.
Combinations
The number of n distinct objects taken r at a time is denoted _nC_r and can be calculated using the following formula.
_nC_r=n!/( n- r)! r!
In total there are 500 boys in the drawing and only 2 will be selected as winners. Let's substitute n= 500 and r= 2 to calculate the number of possible outcomes.
We found that the number of possible outcomes is equal to 124 750. Also, there is only 1 favorable outcome — when Josh and Sokka win the tickets. Now we are ready to calculate the probability.
P=Favorable Outcomes/Possible Outcomes=1/124 750
The probability that Josh and Sokka win the tickets is equal to 1124 750.
