Compound Probabilities and Odds -- Sections 8.8,8.9 --

 Roll two dice at once.   Find the probability of throwing a sum of 10. Find the probability of throwing a sum of 2 or 3.
 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) An experiment consists of throwing two dice, one red and one green.  The reason for using 2 different color dice  is to emphasize that (1,2)  and (2,1) are 2 different throws.
 Solve Step Find the probability of throwing a sum of 10. You can roll   (4,6) , (5,5), or  (6,4) 3 ways to roll a 10. 6 × 6 = 36 different throws. Find the probability of throwing a sum of 2 or 4. You can roll   (1,1) , (1,3),  (2,2) or  (3,1) 1 way to roll a 2 and 3 ways to roll a 4 4 ways total,  È means 'or'

 Roll two dice at once.   Find the probability of throwing a sum of 7. Find the probability of throwing a sum of 7 or 11.
 [Solution]
 Suppose we pick 2 balls out of a box  without replacement. Let's say 5 are red and 7 are blue. What is the probability of picking a red ball then a blue ball?
 Solve Step Pick red first.  Pr(red) = 5/12 There are a total of 12 balls in the box. Then pick blue. Pr(blue) = 7/11 Notice it is not 7/12 since once we picked a red ball there is one less ball in the box. Pr(red then blue) = 5/12 × 7/11 = 35/121 These events are not independent.

 Suppose we pick 2 balls out of a box  without replacement. Let's say 3 are red and 5 are blue. What is the probability of picking a red ball then a blue ball?
 [Solution]
 Suppose we pick 2 balls out of a box  with replacement. Let's say 5 are red and 7 are blue. What is the probability of picking a red ball then a blue ball?
 Solve Step Pick red first.  Pr(red) = 5/12 There are a total of 12 balls in the box. Then pick blue.  Pr(blue) = 7/12 The number of balls is not reduced because the question said with replacement. The first ball is put back in the box. Pr(red then blue) = 5/12 × 7/12 = 35/144 These events are independent.
 Suppose we pick 2 balls out of a box  with replacement. Let's say 8 are red and 4 are blue. What is the probability of picking a red ball then a blue ball?
 [Solution]
 The odds of winning a race is 3 to 2.  Find the probability of winning.
 If the odds in favor of an event are a to b,  the probability of the event is Solve Step a = 3 and b = 2 The probability of winning is 60%.
 The probability of winning a race is 0.70.  Find the odds in favor of winning.
 [Solution]

Tutorials and Applets by
Joe McDonald