制作应用数学系概率统计课程组.pptVIP

Application 1 Question What is the probability of rolling an even number with one dice? a number greater than 3 with one dice? Solution The sample space for rolling one dice is S = {1,2,3,4,5,6}. Lets say event A is rolling an even number and B is rolling a number greater than 3. then, A= {2,4,6} and B= {4,5,6} a) P(A) = = = b) P(B)= n(B)/n(S) = 4/6 = 2/3 Application 2 Question There are three white balls and 5 red balls in the plastic bag. What is the probability of choosing a white ball? (event A) two red balls? (event B) a white ball and three red balls? (event C) Solution (a) There are 8C1 ways to choose any one ball from the plastic bag. Since there are 3 white balls, there are 3C1 ways of choosing a white ball. Thus, P(A) = 3C1/ 8C1 = 3/8 (b) P(B) = 5C2 /8C2 = 5/14 (c) There are 8C4 ways of choosing 4 balls from 8. Also, there are 3C1 * 5C3 ways of choosing one white ball and three red balls. Thus, P(C) = (3C1 * 5C3 ) / 8C4 = 3/7 Check your understanding!! Q.1 What is the probability of choosing a vowel from the alphabet? (★) Q.2 There are two dice and they are rolled simultaneously. What is the probability of rolling (a) the same numbers, (b) the numbers whose sum is 7 (c) the numbers whose sum is less than or equal to 5. (★ ★) Q.3 A dice is rolled twice. What is the probability of having the second number that is greater than the first one? (★ ★★) Answer Key Q.1 Among 26 alphabets, 5 of them are vowels. Therefore, P(A) = n(A)/n(S) = 5/26 Q.2 There are 36 outcomes in total as each dice has 6 numbers. (6C1 * 6C1). Part A: one can have (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). Since n(A)=6, the P(A) = 6/36 = 1/6 Part B: There are 6 possible ways of getting a sum of 7. Thus, P(B) = 6/36 = 1/6 Part C: n(c) = 10 ( all the purple -coloured squares) Thus, P(C) = 10/36 = 5/18 课件制作：应用数学系 概率统计课程组 概率论与数理统计 第一章 随机事件及其概率 1.1 基本概念 1.1.1 随机现象 1.1.2 随机现象的统计规律性 1.1.3 样本空间 1.1.4