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# Lesson 11 5 b notes dependent & independent events

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### Lesson 11 5 b notes dependent & independent events

1. 1. Name ___________________________________ Date ______________________Mrs. Labuski & Mrs. Rooney Period _______ Lesson 11-5B Independent & Dependent EventsVOCABULARY DEFINITION EXAMPLE Pick One Pick TwoINDEPENDENT EVENTS Pick One Pick Two DEPENDENT EVENTSDetermine whether the following events are independent or dependent.1. Kathy draws a 4 from a set of cardsnumbered 1-10 and rolls a 2 on a number cube. ___________________2. John chooses a book from the shelf to read, and thenBrian chooses a different book from the remaining books. ___________________3. Adrian chooses a baseball card from a stack and doesnot return it to the stack. Then Jenna chooses a card from stack. _______________4. Mike draws a 7 from ten cards numbered1 through 10. He replaces the card. Then Allison draws a 5. _________________
2. 2. To find the probability of Two Independent Events: P(A and B) = P(A) • P(B)probability probability probabilityof both events of first event of second eventFind the probability of rolling a 3 on a die & the spinner shown landing on A. P(3 and A) = P(3) • P(A) P(3 and A) = P(3 and A) =The probability of rolling a 3 and the spinner landing on A is _________________.Now you try: Find the probability of each event for the spinners shown.1. The spinners land on 1 and E. 2. The spinners land on even number and A. P(1 and E) P(even number and A3. The spinners land on an odd number and A, B, C, or D. P(odd number and A,B,C,D)
3. 3. To find the probability of Two Dependent Events: P(A and B) = P(A) • P(B after A)probability probability probability of second eventof both events of first event after the first event has occurredA bag contains 2 black marbles and 3 white marbles.Find the probability of drawing a black marble and puttingit aside and then a drawing a white marble. P(black and white) = P(black) • P(white after black) P(black and white) = P(black and white) =The probability of drawing a black marble and then a white marble is ___________.Now you try: Find the probability of each event when after the first draw you donot return the marble to the bag.1. P(white and black) _____________ 2. P(2 white marbles) _____________Nicole has 10 coins in her purse: 3 pennies, 3 nickels, 2 dimes, and 2 quarters.Nicole draws one coin from her purse and puts it on the counter.3. What is the probability that Nicole 4. What is the probability that Nicole will draw a penny and a dime? will draw a quarter and a nickel?
4. 4. Name ___________________________________ Date ______________________Mrs. Labuski & Mrs. RooneyPeriod _______ Lesson 11-5B Independent & Dependent EventsVOCABULARY DEFINITION EXAMPLE Pick One Pick Two The occurrence of one event has noINDEPENDENT effect on the EVENTS probability that the second event will You pick a marble from the bag and then you put it back occur. before the second pick. Pick One Pick Two The occurrence of one event has an DEPENDENT effect on the EVENTS probability that the second event will You pick a marble from the bag and then you do not put it occur. back before the second pick.Determine whether the following events are independent or dependent.1. Kathy draws a 4 from a set of cardsnumbered 1-10 and rolls a 2 on a number cube. independent2. John chooses a book from the shelf to read, and thenBrian chooses a different book from the remaining books. dependent3. Adrian chooses a baseball card from a stack and doesnot return it to the stack. Then Jenna chooses a card from stack. dependent4. Mike draws a 7 from ten cards numbered1 through 10. He replaces the card. Then Allison draws a 5. independent
5. 5. To find the probability of Two Independent Events: P(A and B) = P(A) • P(B)probability probability probabilityof both events of first event of second eventFind the probability of rolling a 3 on a die & the spinner shown landing on A. P(3 and A) = P(3) • P(A) 1 • 1 P(3 and A) = 6 5 1 P(3 and A) = 30 1The probability of rolling a 3 and the spinner landing on A is ____30___________.Now you try: Find the probability of each event for the spinners shown.1. The spinners land on 1 and E. 2. The spinners land on even number and A. P(1 and E) P(even number and A)= 1 • 1 = 1 3 • 0 = 0 4 5 20 63. The spinners land on an odd number and A, B, C, or D. P(odd number and A,B,C,D) 2• 4= 8 =4 4 5 20 5 (You can cross reduce before multiplying!)
6. 6. To find the probability of Two Dependent Events: P(A and B) = P(A) • P(B after A)probability probability probability of second eventof both events of first event after the first event has occurredA bag contains 2 black marbles and 3 white marbles.Find the probability of drawing a black marble and puttingit aside and then a drawing a white marble. P(black and white) = P(black) • P(white after black) 2 • 3 P(black and white) = 5 4 P(black and white) = 6 = 3 20 10 3The probability of drawing a black marble and then a white marble is __10______.Now you try: Find the probability of each event when after the first draw you donot return the marble to the bag.1. P(white and black) _____________ 2. P(2 white marbles) _____________ 3• 2= 6 =3 3• 2= 6 =3 5 4 20 10 5 4 20 10 (You can cross reduce before multiplying!)Nicole has 10 coins in her purse: 3 pennies, 3 nickels, 2 dimes, and 2 quarters.Nicole draws one coin from her purse and puts it on the counter.3. What is the probability that Nicole 4. What is the probability that Nicole will draw a penny and a dime? will draw a quarter and a nickel? P(penny and dime) = P(quarter and nickel) = 3• 2= 6 = 1 2• 3= 6 = 1 10 9 90 15 10 9 90 15