Continued

 From a group of 7 men and 6 women, five people are to be selected to form a committee so that at least 3 men on the committee. In how many ways can it be done? What are the possible scenarios 3 men and 2 women, 4 men and 1 woman, or 5 men ( 7 C 3 x 6 C 2 ) + ( 7 C 4 x 6 C 1 ) + ( 7 C 5 ) - but why do we add here? ( ) 756

 In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? The word 'LEADING' has 7 different letters. But, when we pair all the vowels together (EAI) they count as 1 letter So there are 5 letters → 5! = 120 combinations But the vowels can also be rearranged, so → 3! = 6 When we combine these two we get 120 x 6 = 720 possible solutions

 In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.  Let us mark these positions as under:  (1) (2) (3) (4) (5) (6) Now, 3 vowels can be placed at any of the three places marked 1, 3, 5.  Number of ways of arranging the vowels = 3 P 3 = 3! = 6. Also, the 3 consonants can be arranged at the remaining 3 positions.  Number of ways of these arrangements = 3 P 3 = 3! = 6. Total number of ways = (6 x 6) = 36.

StuStaffTotal American European Asian Total ) What is the probability that the driver is a student?

StuStaffTotal American European Asian Total ) What is the probability that the driver drives a European car?

StuStaffTotal American European Asian Total ) What is the probability that the driver is staff and drives an Asian car?

StuStaffTotal American European Asian Total ) What is the probability that the driver drives an American or Asian car? Disjoint?

StuStaffTotal American European Asian Total ) What is the probability that the driver is staff or drives an Asian car? Disjoint?

StuStaffTotal American European Asian Total ) If the driver is a student, what is the probability that they drive an American car? Condition

StuStaffTotal American European Asian Total ) What is the probability that the driver is a student if the driver drives a European car? Condition

Example 19: Management has determined that customers return 12% of the items assembled by inexperienced employees, whereas only 3% of the items assembled by experienced employees are returned. Due to turnover and absenteeism at an assembly plant, inexperienced employees assemble 20% of the items. Construct a tree diagram or a chart for this data. What is the probability that an item is returned? If an item is returned, what is the probability that an inexperienced employee assembled it? P(returned) = 4.8/100 = P(inexperienced|returned) = 2.4/4.8 = 0.5

ReturnedNot returned Total Experienced Inexperienced Total

Only 5% of male high school basketball, baseball, and football players go on to play at the college level. Of these, only 1.7% enters major league professional sports. Of the athletes that do not play college sports, only 0.1% enters major league professional sports. What is the probability that a high school athlete will play professional sports? What is the probability that a high school athlete does not play college sports if he plays professional sports? Play collegeNot play college 1.7% of 50 total Play pro Not play pro Total Make up a population size! 1.7% of 50 5% of 1000 P(play pro) = P(play college & Play pro) or P(not play college & play pro) =.05(.017) + (.95)(.001) =.0018 P(not play college | plays pro) = P(not play college & play pro) / P(play pro) =.95/1.8 =.5278