You and your mom enter a drawing with 3 different prizes. A total of 9 people entered the drawing, and prizes are awarded randomly.There are 504 ways to award the prizes.What is the probability that you win first prize and your mom wins second prize?A.B.C.D.
Question
You and your mom enter a drawing with 3 different prizes. A total of 9 people entered the drawing, and prizes are awarded randomly.There are 504 ways to award the prizes.What is the probability that you win first prize and your mom wins second prize?A.B.C.D.
Solution
To solve this problem, we need to understand that the probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.
Step 1: Identify the total number of outcomes. In this case, we are told there are 504 ways to award the prizes.
Step 2: Identify the number of favorable outcomes. This is where we need to do a bit of calculation.
The probability that you win the first prize is 1 out of 9 (since there are 9 people in total).
The probability that your mom wins the second prize (given that you've already won the first prize) is 1 out of 8 (since there are now only 8 people left).
So, the total number of favorable outcomes is 1/9 * 1/8 = 1/72.
Step 3: Calculate the probability.
The probability is therefore 1/72 divided by 504, which simplifies to approximately 0.00023148.
So, the probability that you win first prize and your mom wins second prize is approximately 0.00023148.
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