1. 7.4 Probability of Independent Events 4/17/2013

2. 2. What is the number of unique 4-digit ATM PIN codes if the first number cannot be 0? The numbers to choose from are 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9 1 st digit 2 nd digit 3 rd digit 910 ● ● ● 4 th digit Since 0 can’t be the 1 st number = 9000

3. Probability Definition: Formula: How it is written:

4. You roll a 6-sided die whose sides are numbered 1 through 6. Find the probability of a.) rolling a 4 b.) rolling an odd number and c.) rolling a number less than 5.

6. 14. At the time of your turn, a particular Scrabble bag contains 5 Es, 3 Rs, 4 Os, and 5 As. What is the probability that you will pull an R? The bag contains 5+3+4+5 = 17 letters Number of ways it can happen: 3 Rs Number of possible outcomes: 17

7. A bag of marbles contains 9 large green marbles, 4 large purple marbles, 5 small green marbles, and 4 small yellow marbles. If you draw a marble at random, what is the probability that you will draw a green marble, given that it is large? The bag contains 9+4 = 13 LARGE marbles Number of ways it can happen : 9 LG Number of possible outcomes: 13

8. 2 or more events that do not have an effect on the outcomes of each event. If A and B are independent events, then P(A and B) = P(A) P(B) Probability of A and B occuring. Definition: Probability of Independent Events: Independent Events Multiply the probability of each event.

9. You flip a coin four times where one side is heads and the other side is tails. What is the chance that you will flip heads the first two times and tails the second two times.

10. Or Use P(A and B) = P(A) P(B)

11. 18. A jar contains 20 red M&Ms, 23 yellow M&Ms, 19 green M&Ms, 15 blue M&Ms, and 17 brown M&Ms. What is the probability of pulling a yellow M&M, replace it in the jar, and then pulling a green M&M? The jar contains 20+23+19+15+17 = 94 M&Ms Number of ways it can happen : 23 Yellow M&Ms Number of ways it can happen : 19 Green M&Ms Number of possible outcomes: 94

12. A random number generator selects three digits from {0, 1, …, 9}. What is the probability that all three numbers are less than or equal to 4? Numbers less than or equal to 4: 0, 1, 2, 3, 4 Number of ways it can happen : 5 Number of possible outcomes: 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

13. The official weather forecast calls for a 30% chance of rain Saturday, a 40% chance rain Sunday, and a 50% chance rain Monday. What is the probability that it DOES NOT rain on any of those days?

14. Homework WS 7.4 Odd problems only