Lesson 11.9 Independent and Dependent Events

Goal Statement will find the probability that event A and event B occur Motivating the Lesson: Place 5 prizes in a bag (with 2 highly desired prizes). Ask what the probability of selecting the favored prizes is. (2/5) Select one of the favored prizes and remove from the bag. Ask students for the prob that the next prize selected will be the favored one. (1/4) Discuss why this prob depends on the result of the first selection.

Motivating the Lesson Place 5 prizes in a bag (with 2 highly desired prizes). Ask what the probability of selecting the favored prizes is. (2/5) Select one of the favored prizes and remove from the bag. Ask students for the prob that the next prize selected will be the favored one. (1/4) Discuss why this prob depends on the result of the first selection.

Dictionary dependent events: -when getting one event affects the probability of getting the other event independent events: -when getting one event does not affect the probability of getting the other event

LET’S TRY Independent: result of 1st coin doesn’t affect result of 2nd. Dependent: did not replace the 1st name, so fewer names in hat for 2nd draw

Try Independent Dependent 3. You randomly draw a marble from a bag. Then you draw a second marble without returning the first one. 4. You roll a 3 on a number cube, then you roll a 3 again.

Independent Events You roll a number cube and toss a coin. a) Why is this an independent event experiment? b) What is the probability of rolling an odd number and getting heads? Independent 1/4

Independent Events You roll a number cube and toss a coin. a) Why is this an independent event experiment? b) What is the probability of rolling an odd number and getting heads? P(odds, heads) = 3/6 x ½ = 3/12 or ¼ Independent b) 1/4

Finding the Probability of Independent Events A computer randomly generates 4-digit passwords. Each digit can be used more than once. a) Why is this an independent event experiment? b) What is the probability that the first two digits in your password are both 1? Digits can be used more than once P(1 and 1) = 1/10 x 1/10 = 1/100

Finding the Probability of Independent Events A computer randomly generates 4-digit passwords. Each digit can be used more than once. a) Why is this an independent event experiment? b) What is the probability that the first two digits in your password are both 1? c) What is the probability that all four digits are 1? Digits can be used more than once P(1 and 1) = 1/10 x 1/10 = 1/100 P(1 and 1 and 1 and 1) = 1/10 x 1/10 x 1/10 x 1/10 = 1/10,000

If each digit can be used only once, are the events still independent If each digit can be used only once, are the events still independent? Explain. No. If each digit can be used only once, when you generate a digit, there is one digit less remaining to be generated for the next digit, which affects the results of the second, third and fourth digit. So, the events are dependent.

A bag contains 5 red marbles and 5 blue marbles A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble. Are these dependent or independent events? Explain to a partner. Dependent. Because you don’t replace the first marble, the probability that the second marble is a certain color is affected by the color of the first marble that you draw.

A bag contains 5 red marbles and 5 blue marbles A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble. What makes this more complicated to calculate? The fractions will not represent the amount of colors left in the bag when one is taken out.

A bag contains 5 red marbles and 5 blue marbles A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble. What makes this more complicated to calculate? Because the events are dependent, the probability that you draw a blue marble after drawing a red marble is written as: P(blue given red) The fractions will not represent the amount of colors left in the bag when one is taken out.

A bag contains 5 red marbles and 5 blue marbles A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble. What makes this more complicated to calculate? Because the events are dependent, the probability that you draw a blue marble after drawing a red marble is written as: P(blue given red) The fractions will not represent the amount of colors left in the bag when one is taken out.

Dictionary Probability of Dependent Events P(A and B) = P(A) x P(B given A)

LET’S TRY A jar of jelly beans contains 50 red jelly beans, 45 yellow jelly beans, and 30 green jelly beans. Eric reaches into the jar and randomly select a jelly bean, then select another without putting the first jelly bean back. a) Are these dependent or independent events? b) What is the probability that Eric draws two red jelly beans? Dependent (because don’t replace 1st jellybean)

LET’S TRY A jar of jelly beans contains 50 red jelly beans, 45 yellow jelly beans, and 30 green jelly beans. Eric reaches into the jar and randomly select a jelly bean, then select another without putting the first jelly bean back. a) Are these dependent or independent events? b) What is the probability that Eric draws two red jelly beans? P(red and then red) = P(red) p P(red given red) Dependent (because don’t replace 1st jellybean) P(red and then red) = 50/125 x 49/124 = 2450/15,500 = 0.16 or about 16%

Show Ms Schones An Advisory class consists of 6 girls and 7 boys. To select MSSC reps, two students are chosen at random one at a time. The first student chosen is a girl. What is the probability that both students who are selected are girls? P(girl then girl) = P(girl) x (P(girl given girl) = 6/13 x 5/12 = 30/156 = 0.19 (19%)

Homework Green: pgs.637 – 638: #1 – 8 (all except 5), 9 – 15 (all), 17 Blue: 11.9 Blue WS