You and your mom enter a drawing with 3 different prizes. A total of 8 people entered the drawing, and prizes are awarded randomly.There are 336 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 8 people entered the drawing, and prizes are awarded randomly.There are 336 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 calculate the probability of you winning the first prize and your mom winning the second prize.
Step 1: Calculate the total number of ways to award the first and second prizes.
Since there are 8 people in the drawing, there are 8 ways to award the first prize. After the first prize is awarded, there are 7 remaining people, so there are 7 ways to award the second prize.
So, the total number of ways to award the first and second prizes is 8 * 7 = 56 ways.
Step 2: Calculate the specific case of you winning the first prize and your mom winning the second prize.
There is only 1 way for you to win the first prize (since there's only one of you), and only 1 way for your mom to win the second prize (since there's only one of her).
So, there is 1 * 1 = 1 way for you to win the first prize and your mom to win the second prize.
Step 3: Calculate the probability.
The probability is the number of ways the specific case can occur divided by the total number of outcomes.
So, the probability of you winning the first prize and your mom winning the second prize is 1 / 56.
Therefore, the answer is 1/56.
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