Lesson 3 Dependent and Independent Events When working with 2 separate events, we must first consider if the first event affects the second event. Situation 1 Situation 2 Drawing two cards from a deck without replacement. Drawing two cards from a deck with replacement. A: The first card is a spade A: The first card is a spade B: The second card is a spade B: The second card is a spade How many cards were in the deck on the first draw? How many cards were in the deck on the first draw? How many cards were in the deck deck on the second draw? How many cards were in the on the second draw? Calculate Calculate P(A and B) P(A and B) These are dependent events These are independent events
If the occurrence of event A does not affect the probability that event B occurs, then A and B are independent and we use the formula If the occurrence of event A affects the probability that event B occurs, then events A and B are dependent. For any independent events P(A and B) is found using the formula
Examples: 1. Classify the following events as independent or dependent. Tossing heads on a coin toss and rolling a 6 on a die Out of a deck of 52 cards,two cards are drawn without replacing the first one. The probability that both cards are aces. Out of a deck of 52 cards, the first card drawn is a king and, after replacement, the second card drawn is a queen. A bag contains 10 candies which are of 3 different colors. The probability that Joe picks a red one (then eats it) and the probability that Sue picks a blue one.
2. Two cards are drawn, with replacement, from a shuffled deck of 52 cards. Let A and B represent these events. A: the first card is a 7. B: the second card is a 7. Determine the probability of each event. a) P(A) b) P(B) 3. Two cards are drawn, without replacement, from a shuffled deck of 52 cards. Let A and B represent these events. A: the first card is a 7. B: the second card is a 7. Determine the probability of each event. a) P(A) b) P(B A)
4. Two cards are drawn, with replacement, from a shuffled deck of 52 cards. What is the probability of drawing a king of hearts and the ace of hearts? Use the following to help A: The first card is the king of hearts B: The second card the ace of hearts a) P(A) b) P(B) 5. Two cards are drawn, without replacement, from a shuffled deck of 52 cards. W king of hearts and the ace of hearts? Use the following to help A: The first card is the king of hearts B: The second card the ace of hearts a) P(A) b) P(B A)
6. In one bag there is 2 green balls and 4 white balls. In a second bag there are 3 green balls and 2 white balls. One ball is drawn from each bag. What is the probability of drawing 2 white balls? 7. In one bag there are 2 white balls and 3 yellow balls. In a second bag there are 2 green balls and 1 orange ball. One ball is drawn from each bag. What is the probability of drawing 1 white ball and 1 green ball? 8. The probability that Ashley will pass Math this semester is 0.7 and the probability that she will pass English this semester is 0.9. If these events are independent, what is the probability (to the nearest hundredth) that she will pass Math and English?
Lesson 3 Worksheet, and... 1. A red die and a blue die are tossed. What is the probability that the red die shows a 1 and the blue die shows a 5 or a 6? 2. Two cards are drawn without replacement from a standard deck of 52 cards. Determine the probability of the following events: a) both cards are spades b) both cards are sevens c) neither card is red