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Welcome to a "ThatQuiz" on Probability! #1-4: Determine whether the scenario involves independent or dependent events. #5-6: Find the probability. #7-10: Determine if events A and B are independent. Two events are "independent" if the happening of one event does not affect the happening of the other. Two events are "dependent" if the happening of one event affects the happening of the other. Determine whether the scenario involves independentor dependent events. 1) You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows a one. Dependent events Independent events 2) You flip a coin and then roll a fair six-sided die. Find the probability that the coin lands heads-up and the die shows a 5. P(heads) • P(5) = P(heads and 5) 3) A bag contains 1 red and 3 blue marbles. You randomly pick a marble, and then pick a second marble, without returning the marbles to the bag. Determine whether the scenario involves independentor dependent events. Independent events Dependent events 4) A bag contains 1 red and 3 blue marbles. You randomlypick a marble, and then pick a second marble, withoutreturning the marbles to the bag. What is the probability that both marbles are blue? P(blue) • P(blue) = P(blue, then blue) without replacement Write fractionin simplest form! The probability of an event happening is the chance that it will occur. Probability ranges from 0 (an impossible event)to 1 (a certain event). Probability can be written as a fraction, decimal, or percent. P(event) = the number of favorable events the total number of possible outcomes Find the probability. Write your answer as a fraction in simplest form. 5) You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a six. P(5 on first roll) P(6 on second roll) • = P(5, then 6) 6) There are eight shirts in your closet. Four are blue and four are green. You do laundry at the end of the week.On Monday, you randomly pick a shirt to wear. On Tuesday you pick a different shirt. Find the probability of wearing a blue shirt on both days. Find the probability. Each fraction should be written in simplest form. P(blue on Mon) P(blue on Tues) • = P(blue on both days) From context, events are independent if the outcome of thefirst event doesn't influence the outcome of the second event. For example, rolling a single die and flipping a coin. Mathematically, when two events A & B are independent, P(A and B) = P(A) • P(B) 7) P(A) = 2/5; P(B) = 1/5; P(A and B) = 2/25 Determine if events A and B are independent. A and B are independent events. A and B are dependent events. 8) P(A) = 2/5; P(B) = 1/4; P(A and B) = 1/25 Determine if events A and B are independent. A and B are independent events. A and B are dependent events. Given: P(A') = To determine the probability of "not A", we use the complement rule. 9) 1 3 What is P(A)? 10) P(A') = 3/4; P(B) = 3/10; P(A and B) = 3/40 Determine if events A and B are independent. A and B are independent events. A and B are dependent events. |