Section 7.3 and 7.4 Probability of Independent Events


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1 Section 7.3 and 7.4 Probability of Independent Events Grade 7 Review Two or more events are independent when one event does not affect the outcome of the other event(s). For example, flipping a coin and rolling a die are independent events. There are a few ways to represent all the outcomes that are possible for 2 or more independent events. The two most common ways are using a chart (2 events) or a tree diagram (2 or more events). Example 1. a) Create a tree diagram to show the possible outcomes for flipping a coin and rolling a 4 sided die labelled 1,2,3, and 4. b) What is the probability of tossing tails and rolling a 2? c) What is the probability of tossing heads or tails and rolling an odd number? Example 2. a) Create a table to show the possible outcomes for tossing two 6 sided dice. b) What is the probability of rolling two even numbers?
2 In example 1 above, what are the probabilities of each single event below? a) P(Tails) b) P(Rolling a 2) How could we get the answer to part b) using the two individual probabilities above? Probability of Independent Events When two or more events are independent then we can calculate the probability of both (or all) events happening together by the probability of each individual event. P(A and B) = P(A and B and C)=
3 Example 2. A bag contains 8 blue marbles, 7 green marbles and 5 white marbles. You are going to reach into the bag and grab one marble then put the marble back before getting the next marble. a) What is the probability picking a green marble then a white marble? b) What is the probability of picking two blue marbles? c) What is the probability that the first marble is not white, then the second marble is white? d) What is the probability of picking one marble of each colour? Example 4. Frank has two decks of cards. He is going to pick a card from each deck. What is the probability of each event? a) He picks a 2 of diamonds and a 10 of clubs? b) He picks a red card and a spade? c) He picks a face card (J, Q, or K) and a heart.
4 Example 5. Today there is a 40% probability of flurries in Pout aux Basque, a 60% probability of flurries in Deer Lake, and a 50% probability of flurries in Corner Brook. What is the probability that there will be flurries in all three towns today? Example 6. The lock on a briefcase has four dials with digits from 0 to 9. What is the probability that someone will guess the correct combination on the first try? Example 7. Nathan didn t study for his math assignment. There are 3 multiple choice on the test that he does not know how to do, so he is going to guess the answers. Each question has 4 possible answers. What is the probability of each of the following: a) He gets all 3 questions correct. b) He gets the first two correct. c) He gets 3 of the questions wrong.
5 Section Worksheet 1. What is the probability of tossing two coins and having them both show heads? 2. Every time Mr. Coleborn throws a ball of paper in the garbage can, the probability the ball goes in the can is 4 3. What is the probability he misses 2 times in a row? 3. A spinner has 3 congruent sectors coloured red, blue, and yellow. The pointer is spun and a 4 sided die labelled 1, 2, 3, and 4 is rolled. a) Find the probability of each event: i) Landing on red and rolling a 4. ii) Landing on blue and rolling an even number. iii) Not landing on yellow and rolling an odd number. 4. An experiment consists of picking a card from a standard deck of playing cards and drawing a counter from a bag that contains 5 counters: 2 blue, 2 white, and 1 red. Find the probability of each event: a) Picking a spade and drawing a blue counter. b) Picking a red card and drawing a red counter. c) Picking a face card and not drawing a white counter. d) Picking a diamond and drawing a green counter.
6 5. A regular 6sided die is rolled three times. Find the probability of each event: a) Three 6s in a row b) 5, 1, even c) Odd, greater than 2, 5 6. Each time Parker shoots a free throw in basketball, he has an 80% chance of making the shot. Suppose he is given 3 free throws. Find the probability of each event. a) Makes the basket, misses the basket, c) Misses all 3 shots makes the basket b) Makes all 3 shots d) Misses the first two shots and makes the third 7. Gretchen knows the combination to a bank vault lock is two letters followed by two numbers. a) What is the probability that Gretchen guesses the combination on her first attempt? b) Suppose she knows the combination starts with the letter M. What is the probability she guesses the combination on her first attempt? 8. Karen, Gavin, Nasra, and Ali each have a deck of playing cards. Each student randomly draws a card from the deck. Find the probability of each event: a) Each student draws a club. b) Karen draws a red card, Gavin draws a king, Nasra draws a black card, and Ali draws the 2 of clubs. c) Karen draws a heart, Gavin draws a heart, Nasra draws a face card, and Ali draws an ace.
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