Subject: Probability and Statistics

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Let us solve more problems on compound probability! Activity 9. Solve the following problems: 1) Out of the 45 books in the bookshelves, 18 are mathematics books, 10 are science books, 9 are history books and 8 are story books. If you pick one book at random, what is the probability that it is a science or mathematics book? 2) In a particular class, 78% of the students have a smartphone, 38% have a smartphone and a tablet, and 3 % have neither a smartphone nor a tablet. Find the probability that a randomly selected student has a a) tablet? b) tablet or a smartphone? c ) smartphone but does not have a tablet? 3) In a junior high school completing class of 510 students, 110 are on the Science, Technology and Engineering (STE) Program. Of these, 78 of the STE Program students and 112 of the non-STE program students will take STEM as their senior high school track. A student is selected from the class, what is the probability that the student chosen will: a) take STEM as their senior high school track? b) not take STEM and on the Science, Technology and Engineering Program? c) take STEM or on the Science, Technology and Engineering Program? 4) A sample survey results of the talents of some grade 10 students are given in the following table. Dancing Singing Total Male 28 24 Female 32 26 Total If a student is selected at random from this group, what is the probability that the student selected is a a) male? b) female whose talent is singing? c) student whose talent is dancing? d) male whose talent is singing?1) If A = (2, 4, 6, 8, 10, 12, 14, 16) and B= (3, 6, 9, 12, 15), find n(A U B). A) 0 B) 2 C) 8 D) 11 2) Which of the following is a true statement? A) The probability of a certain event is 0. B) The probability that an event will happen is from 0 to 1. C) The closer is the probability of an event to 0, the more likely it is to happen. D) In an experiment with outcome that are equally likely to happen, the probability of an event is the ratio that compares the number of favorable outcomes to the number of not favorable outcomes. 3) Which of the following does NOT illustrate compound events? A) Getting a 4 or an even number in rolling a standard die. B) Choosing a female and a grade 10 student. C) Picking a blue or a pink dress in the closet. D) Head turning up in tossing a coin once. 4) How many possible outcomes are there in tossing a coin once and rolling a die once? A) 3 B) 6 C) 8 D) 12 5) There are 22 apples and 24 oranges in a basket. If a fruit is picked at random, what is the probability of picking an apple? B) 11 C ) 11 A) D) 6 23 11 6) Find the probability of getting at least 2 heads in tossing a coin thrice? Al 2 B) - uil - D) - For items 7 & 8. In tossing a six - sided die, let A be the event of getting a factor of 4 and B be the event of getting an even number. 7) What is An B? A) {1, 2, 4} B) (2, 4, 6) C) (2,4) D) {1, 2, 4, 6}8) What is the cardinality of A U B? A) 4 B) 3 C) 2 D) 1 9) A box contains 8 black marbles, 12 white marbles, and 5 yellow marbles. If a marble is drawn at random, what is the probability of getting a black or a white marble? 13 A) 17 12 25 B) 25 C ) 25 D) 10) Find the probability of choosing the letter M or the letter E from the word "MATHEMATICS". A) B) C) D) 6 11 1 1) A die is rolled once. What is the probability of getting a result which is an odd number and a factor of 6? A) NI- B ) 3 12) Two fair dice are rolled once. What is the probability of getting a sum that is greater than 6 but less than 9? A) 5 18 B) 7 D) 11 WIN C ) 18 36 For items 13 & 14. From a survey of habits, 52% of students interviewed said that they surf the internet, 28% read pocketbooks, and 15% surf the internet and read pocketbooks. If a student is chosen from those who were interviewed, find the probability that this student 13) surf the internet or read pocketbooks. A) 80% B) 67% C) 65% D) 15% 14) does NOT surf the internet nor read pocketbooks. A) 15% B) 35% C) 65% D) 85% 15) In a graduating class of 100 students, 65 will study mathematics, 70 will study physics, and 40 will study both mathematics and physics. If one of these students is selected at random, find the probability that the student will study physics but NOT mathematics. A) B) C) D) 10 20 20