Independent & Dependent Events

1. Independent & Dependent Events Probability

2. Definitions: • Events are independent events if the occurrence of one event does not affect the probability of the other. • Events are dependent events if the occurrence of one does affect the probability of the other.

3. Determine if the events are dependent or independent. • Getting tails on a coin toss and rolling a 6 on a number cube. • Tossing a coin does not affect rolling a number cube, so the two events are independent. • Getting 2 red gumballs out of a gumball machine. • After getting one red gumball out of a gumball machine, the chances for getting the second red gumball have changed, so the two events are dependent. • Rolling a 6 two times in a row with the same number cube. • The first roll of the number cube does not affect the second roll, so the events are independent.

4. 12 12 12 18 · · = Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box. What is the probability of choosing a blue marble from each box? P(blue, blue, blue) =

5. Find each probability if you spin both spinners. • P (white, A) • P (striped, A) • P (not striped, B) • P (not white, B) P = 1/5(1/3) = 1/15 P = 2/5(1/3) = 2/15 2/5 P = 3/5(2/3) = 6/15 = P = 4/5(2/3) = 8/15

6. To calculate the probability of two dependent events occurring, do the following: 1. Calculate the probability of the first event. 2. Calculate the probability that the second event would occur if the first event had already occurred. 3. Multiply the probabilities.

7. Find each probability if you pick a card, do not replace it, the pick a second card. • P(black, then white) • P(black, then black) • P(white, then white) P = 5/8 * 3/7 = 15/56 1 P = 5/8 * 4/7 = 5/14 2 1 3/28 P = 3/8 * 2/7 = 4

8. If the letters to the word Dependent are placed in a box… If two letters are chosen at random, what is the probability that both letters are vowels? P(vowel, vowel) = 3/9 * 2/8= 1/12 1/3 * 1/4=