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# Using Tree to Solve Probability Problems

Using Tree to Solve Probability Example 1
There are a pair of green gloves and a pair of blue gloves mixed together in a black box. All the gloves have the same size and material. If you picked one at first time, and then pick another at second time, what is the probability that you pick exactly a pair of gloves?
Solution
Let gl is green-left, gr is green-right, bl is blue-left, br is blue-right. If you first time pick gl, second time you can only pick gr or bl or br, then gl and gr is a pair of gloves. If you first time pick bl, then second time you can only pick gl or gr or br, then bl and br is a pair of gloves. There are 4 ways to pick a pair of gloves, gl - gr, gr - gl, bl - br, br - bl. There are total of 12 coutcomes, gl - gr, gl - bl, gl - br, gr - gl, gr - bl, gr - br, bl - gl, bl - gr, bl - br, br - gl, br - gr, br -bl. The probability that pick a pair of glove is:
Solution>
Using Tree to Solve Probability Example 2
Box A has two cards named 1 and 2 inside, box B has three cards named 3, 4, 5, inside, box C has two cards named 6 and 7 inside. All cards in the three box are the same size and the same material. Shaked each box and pick one card from each box. Answer the following questions:
1. What is the probability of getting a sum of 11?
2. What is the probability of getting a sum of 12?
Solution