Probability Assignment.docx - Probability Assignment 1 During a recent survey of ethnic backgrounds of 1000 people in a large city 513 were Canadian 148

Probability Assignment.docx - Probability Assignment 1...

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Probability Assignment 1. During a recent survey of ethnic backgrounds of 1000 people in a large city, 513 were Canadian, 148 were French, 72 were African and 56 were Asian and the remainder were from other groups. Calculate the probability that a person, selected at random from the population has: a. A Canadian background? Probability (Canadian) = Number of Favorable Outcomes/Total Number of Possible Outcomes Probability (Canadian) = 513/1000 Probability (Canadian) = 0.513 Therefore, the probability that a person, selected at random from population that has a Canadian Background is 0.513 b. An African background? Probability (African) = Number of Favorable Outcomes/Total Number of Possible Outcomes Probability (African) = 72/1000 Probability (African) = 0.072 Therefore, the probability that a person, selected at random from population that has an African background is 0.072 c. An “other” background? 1000 – (513 + 148 +72 + 56) = 1000 1000 – 789 = 211 There are 211 people within the “other” groups in 1000 people in a large city. Probability (Other) = Number of Favorable Outcomes/Total Number of Possible Outcomes Probability (Other) = 211/1000 Probability (Other) = 0.211 Therefore, the probability that a person, selected at random from a population that has an “other” background is 0.211 2. A spinner is divided into three equally sized regions as shown. The spinner is spun twice. For each probability you determine, express your answer as a fraction, decimal and percent. a. What is the probability of spinning A on the first spin? Probability = Number of Favorable Outcomes/Total Number of Possible Outcomes Probability = 1/3 Probability = 0.3333 Probability = 0.3333 x 1000 Probability = 33.33% Therefore, the probability is 1/3 in fraction form, 0.3333 in decimal form, and 33.33% in percent.
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b. Draw a tree diagram to represent the sample space for both spins. Spin 1 Spin 2 Outcome A A,A A B A,B B A,B A B,A B B B,B B B,B A B,A B B B,B B B,B c. What is the probability of spinning A followed by B? Probability = Number of Favorable Outcomes/Total Number of Possible Outcomes Probability (A then B) = 2/9 Probability (A then B) = 0.2222 Probability (A then B) = 0.2222 x 1000 Probability (A then B) = 22.2% Therefore, the probability is 2/9 in fraction form, 0.2222 in decimal form and 22.2% in percentage form. d. What is the probability of getting the same letter on both spins? Probability (Both spins) = Number of favorable outcomes/Total Number of Possible Outcomes + Number of Favorable Outcomes/Total Number of Possible Outcomes Probability (Both spins) = 1/9 + 4/9 Probability (Both spins) = 5/9 Probability (Both spins) = 0.5555 x 100 Probability (Both spins) = 55.5% Therefore, the probability that the same letter on both spins is 5/9 in fraction form, 0.5555 in decimal form, and 55.5% in percentage form.
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