Answer:the probability that all the players on the court are boys is approximately 0.0833 or 8.33%.
Explanation:
To find the probability that all the players on the court are boys, we need to consider the total number of possible combinations of players on the court and the number of combinations where all the players are boys.
First, let's calculate the total number of possible combinations of players on the court. Since there are 7 boys and 3 girls on the team, the total number of players is 7 + 3 = 10. And we need to select 5 players to play on the court.
We can use the combination formula to calculate this. The formula for combinations is:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items selected.
Using this formula, we can calculate the total number of combinations:
10C5 = 10! / (5!(10-5)!)
= (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)
= 252
So, there are 252 possible combinations of players on the court.
Next, let's calculate the number of combinations where all the players are boys. Since there are 7 boys on the team, we need to select all 5 boys to play on the court.
Using the combination formula again, we can calculate this:
7C5 = 7! / (5!(7-5)!)
= (7 * 6) / (2 * 1)
= 21
So, there are 21 combinations where all the players on the court are boys.
Finally, to find the probability, we divide the number of favorable outcomes (all boys) by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 21 / 252
= 1/12
= 0.0833 (rounded to four decimal places) or 8.33% (rounded to two decimal places)
Therefore, the probability that all the players on the court are boys is approximately 0.0833 or 8.33%.