Problems

1. Xiao Ming and Da Qing play a game. They have two identical coins. Each one takes turns to throw the coins one after another. If two heads apprear, Xiao Ming wins. If one head and one tail appear, Da Qing wins. If two tails appear, no body wins. Is this a fair game?

2. Xiao Ming and Da Qing play a game. They have two identical coins. Each one takes turns to throw the two coins together. If two heads apprear, Xiao Ming wins. If one head and one tail appear, Da Qing wins. If two tails appear, no body wins. Is this a fair game?

3. Each dice has six faces numbered by 1, 2, 3, 4, 5 and 6. Throw two dices one after another. What is the probability of the summation of the displayed two numbers is an even number?

4. Each dice has six faces numbered by 1, 2, 3, 4, 5 and 6. Throw two dices together. What is the probability of the summation of the displayed two numbers is an even number?

5. Each dice has six faces numbered by 1, 2, 3, 4, 5 and 6. Xiao Ming throws a dice and gets a number \(p\). Da Qing throws a dice and gets a number \(q\). (1) what is the probability that equation \(x^2 + px + q =0\) has two different real solutions? (2) what is the probability that equation \(x^2 + px + q =0\) has two identical real solutions?

Solutions