AMC 8 Daily Practice Round 1
Complete problem set with solutions and individual problem pages
Vendors often run lottery games at the school gate. One vendor has a black bag containing balls of different colors: red, yellow, green, and the rest white. After mixing them thoroughly, the rule is: each draw costs dollars for ball.
Drawing a red ball wins a prize worth dollars.
Drawing a yellow ball wins a prize worth dollars.
Drawing a green ball wins a prize worth dollars.
Drawing a white ball wins no prize.
If you spend dollars to draw balls at the same time, what is the probability of obtaining a prize worth dollars?
- A.
- B.
- C.
- D.
- E.
There are two cases for winning a prize worth dollars:
Case : Drawing one -dollar prize and one -dollar prize, i.e., one red ball and one green ball. The probability of drawing a red ball first and then a green ball, or a green ball first and then a red ball, is the same, giving
Case : Drawing two yellow balls. The probability of drawing the first yellow ball is , and the probability of drawing the second yellow ball is . Thus,
Therefore, the total probability is
