Notes #45 Probability as a Fraction, Decimal, and Percent. As a result of what I learn today, I will be able to
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1 Notes #45 Probability as a Fraction, Decimal, and Percent As a result of what I learn today, I will be able to Probabilities can be written in three ways:,, and. Probability is a of how an event is to. An is something. Example of events: What do you think it means if something has a probability of 0? What do you think it means if something has a probability of 1? The is the range of values from to. (A probability cannot be or greater than.) probability is probability based on (what have happened). probability is probability based on from an (what happened). A is performing an. Examples include rolling a die or spinning a spinner. are the different possibilities in a. outcomes are the sum of that can in an experiment. outcomes are any outcomes that mean your event has. is when outcomes are no longer to happen. An example is a die that is weighted. 2
2 Examples: 1. A card is drawn from an ordinary 52 card pack. What is the probability that the card will be a king? 2. Jason has 20 socks in a drawer. 8 socks are red, 10 socks are blue and 2 socks are green. If a sock is drawn at random, what is the probability that it is green? 3. An unbiased die is thrown and the number on the upward face is recorded. Find the probability of obtaining: (a) a three (b) an even number (c) a prime number. 4. Nine painters are assigned a letter from the word HOLLYWOOD for painting at random. Find the probability that a painter is assigned: (a) the letter Y (b) the letter O (c) the letter H or the letter L (d) the letter Z 3
3 5. A bag contains nine equal sized marbles. Four of the marbles are colored blue and the remaining five marbles are colored red. What is the probability that, when a marble is drawn from the bag: (a) it is blue? (b) it is red? (c) it is neither blue nor red? (d) it is either blue or red? 6. The probability that Jasmine passes her driving test is 2. What is the 3 probability that Jasmine fails? 7. The probability that Ms. Tomasson goes to California is 2 5. What is the probability that Ms. Tomasson doesn t go to California? 4
4 8. A simple die is rolled 100 times and the number five appears 14 times. Find the theoretical probability of rolling a five. Find the experimental probability of rolling a five. 9. Suppose that a blindfolded man is asked to throw a dart at a dartboard. He hits the number six 15 times out of 125 throws. What is the theoretical probability of hitting the number six? What is the experimental probability of hitting the number six? 5
5 Practice Homework #45 Probability as a Fraction, Decimal, and Percent 1. A bag contains 24 discs. 10 discs are red, 9 discs are green and 5 discs are yellow. (a) A disc is chosen at random. Find, as a fraction, the probability of each of the following events. (i) Event A: the disc is red. Answer (b)(i).. (ii) Event B: the disc is red or yellow. Answer (b)(ii).. (iii) Event C: the disc is not yellow. Answer (b)(iii). 2. A bag of 30 sweets contains 8 chocolates, 13 nougats and 9 toffees. A sweet is selected at random. What is the probability that it is a toffee? Answer 3. (a) There are 12 boys and 13 girls in a choir. The teacher chooses one choir member at random. What is the probability that this is a girl? Write your answer as a fraction. Answer (a).. 6
6 9 (b) The probability that Carla arrives at school before is. 20 What is the probability that Carla does not arrive before 08 00? Write your answer as a fraction. Answer (b).. 4. (a) A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange. Susie chooses one piece of fruit at random. What is the probability that she chooses (i) a banana, Answer (a)(i) (ii) a mango? Answer (a)(ii) (b) The probability that it will rain in Switzerland on 1 st September is. State the probability that it will not rain in Switzerland on 1 st September. Answer (b) 6) A single die (six sided number cube) is thrown 100 times and the number 5 appears 14 times. a) Find the experimental probability of throwing a b) Find the theoretical probability of throwing a 5. 7
7 7) The diagram shows a spinner that is divided into exactly eight equal sections. Ryan spins the spinner 260 times and records the results in a table: Number Frequency a) What is the experimental probability of spinning the number 3? b) What is the theoretical probability of spinning the number 6? c) What is the experimental probability of spinning an odd number? d) What is the theoretical probability of spinning a multiple of 3? 8) A survey asked respondents what kind of fuel they used in their cars. The results are displayed below: Type of Fuel Gas Diesel Electricity Other Frequency a) Find the probability that a car chosen at random is powered by electricity. b) Find the probability that a car chosen at random is not powered by gas. 8
2 C. 1 D. 2 4 D. 5 3 C. 25 D. 2
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