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# Probability 3.3

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### Probability 3.3

1. 1. The Addition Rule Chapter 3.3
2. 2. Objectives <ul><li>Determine if 2 events are mutually exclusive </li></ul><ul><li>Use the Addition Rule to find the probability of 2 events </li></ul>
3. 3. Mutually Exclusive Events <ul><li>Two events are mutually exclusive if A and B cannot occur at the same time. </li></ul>A A B B
4. 4. Are these events mutually exclusive? <ul><li>Event A: Roll a 3 on a die </li></ul><ul><li>Event B: Roll a 4 on a die </li></ul><ul><li>yes </li></ul>
5. 5. Are these events mutually exclusive? <ul><li>Event A: Randomly select a male student </li></ul><ul><li>Event B: Randomly select an Auto Tech student </li></ul><ul><li>No, a student can be both male and in Auto Tech </li></ul>
6. 6. Are these events mutually exclusive? <ul><li>Event A: Randomly select a blood donor with type O blood. </li></ul><ul><li>Event B: Randomly select a female blood donor </li></ul><ul><li>No, a blood donor can be both female and type O </li></ul>
7. 7. <ul><li>What is the probability of rolling a 3 or a 4 on a 6-sided die? </li></ul>
8. 8. The Addition Rule <ul><li>The probability that events A or B will occur P(A or B) is given by </li></ul><ul><li>P(A or B) = P(A) + P(B) – P(A-B) </li></ul><ul><li>If events A and B are mutually exclusive, then the rule can be simplified to </li></ul><ul><li>P(A or B) = P(A) + P(B) </li></ul>
9. 9. Find the probability . . . <ul><li>Of selecting a card from a standard deck that is a 4 or an ace . . . </li></ul><ul><li>P(4 or ace) = P(4) + P(ace) </li></ul><ul><li>= 4/52 + 4/52 = 8/52 = 2/13 = .154 </li></ul>
10. 10. Find the probability . . . <ul><li>Of rolling a number less than 3 or an odd number . . . </li></ul><ul><li>These events are not mutually exclusive </li></ul><ul><li>P(less than 3 or odd) = P(less than 3) + P(odd) – P(less than 3 and odd) </li></ul><ul><li>= 2/6 + 3/6 – 1/6 = 4/6 = 2/3 = .667 </li></ul>
11. 11. Sales Volumes <ul><li>This chart shows the volume of sales (in dollars) and the number of months a sales rep reached sales level during the past 3 years. </li></ul>Sales Volume Months 0-24,999 3 25,000-49,999 5 50,000-74,999 6 75,000–99,999 7 100,000-124,999 9 125,000-149,999 2 150,000-174,999 3 175,000-199,999 1
12. 12. Sales Volumes <ul><li>If this sales pattern continues, what is the probability that the sales rep will sell between \$75,000 and \$124,999 next month? </li></ul>Sales Volume Months 0-24,999 3 25,000-49,999 5 50,000-74,999 6 75,000–99,999 7 100,000-124,999 9 125,000-149,999 2 150,000-174,999 3 175,000-199,999 1
13. 13. Sales Volumes <ul><li>A = sales between 75,000 & 99,999 </li></ul><ul><li>B = sales between 100,000 & 124,999 </li></ul><ul><li>P(A or B)=P(A)+P(B) </li></ul><ul><li>= 7/36 + 9/36 </li></ul><ul><li>=16/36 =4/9 =.444 </li></ul>Sales Volume Months 0-24,999 3 25,000-49,999 5 50,000-74,999 6 75,000–99,999 7 100,000-124,999 9 125,000-149,999 2 150,000-174,999 3 175,000-199,999 1
14. 14. <ul><li>In a survey conducted by the National Family Organization, new mothers were asked to rate the difficulty of delivering their first child compared with what they expected. </li></ul><ul><li>If you selected a new mother at random and asked her to compare the difficulty of her delivery with what she expected, what is the probability that she would say that it was the same or more difficult than what she expected? </li></ul>
15. 15. Example 5, p. 144 <ul><li>Use the graph on p. 144 to find the probability that a randomly selected draft pick is not a running back or a wide receiver. </li></ul><ul><li>Define A: Draft pick = running back </li></ul><ul><li>Define B: Draft pick = wide receiver </li></ul><ul><li>P(A or B) =19/255 + 32/255 =51/255 = 1/5 </li></ul><ul><li>P(not RB or WR) = 1 – 1/5 = 4/5 = .8 </li></ul>
16. 16. Turn to page 145 <ul><li>Do questions 1-9, 19 together </li></ul><ul><li>Homework: 10-24 evens </li></ul>