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Independent and Dependent Events. If you consider the outcomes of two events, the events are called compound events . Two compound events are independent events if the occurrence of one does not affect the likelihood the other event will occur.
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If you consider the outcomes of two events, the events are called compound events. Two compound events are independent eventsif the occurrence of one does not affect the likelihood the other event will occur. Two compound events are dependent eventsif the occurrence of one does affect the likelihood the other event will occur.
Tell whether the situation describes independent events or dependent events. (1) You flip the same coin twice. What is the probability that you get tails both times? (2) A bag contains 3 red marbles are 4 blue marbles. You select one marble from the bag, set that marble off to the side, and then select a second marble. What is the probability that both marbles are red?
Tell whether the situation describes independent events or dependent events. (3) When playing a word game, a player randomly chooses letters from a bag. At the beginning of the game, the bag contains 5 each of the letters R, S, T, L, and N and 4 each of the letters A and E. The first player draws letters from the bag. What is the probability that the first player will choose an R and then an E from the bag? (4) You have created a computer program that randomly selects a number from 1 to 40. You run the program two times. What is the probability that the program selects 6 as the first number and 2 as the second number?
Probability of Independent Events For two independent events A and B, the probability that both events occur is the product of the probability of the events.
Examples: In a board game, you spin the spinner below. You spin the spinner twice. What is the probability that you first a 3, and then spin a 7? Again, you spin the spinner twice. What is the probability that you first a an even number, and then spin a prime number?
Probability of Dependent Events For two dependent events A and B, the probability that both events occur is the product of the probability of the first event and the probability of the second event given the first.
Example: The 25 fish in your aquarium are 12 loaches, 7 barbs, and 6 tetras. You want to give 2 fish to a friend. You randomly choose 1 fish from the aquarium, then randomly choose another fish without replacing the first. Find the probability that both are loaches.
