Probability and Counting Rules Sec 4.5 Probability and Counting Rules Bluman, Chapter 4

Review questions: Calculate the following on your calculators 12p5 nc1 for any positive values of n np1 for any positive values of n ncn for any positive values of n npn for any positive values of n nc0 for any positive values of n np0 for any positive values of n Bluman, Chapter 4

Roger’s parents plan to visit 4 of his 8 classes. In How many ways can his parents visit his classes at Back to School Night? In How many ways can his parents visit his classes at Parent conferences. Bluman, Chapter 4

Bluman, Chapter 4

Multiple choice examples http://www.indiabix.com/aptitude/permutation-and-combination/ Comboniation and Permuation practice problems Bluman, Chapter 4

4.5 Probability and Counting Rules The counting rules can be combined with the probability rules in this chapter to solve many types of probability problems. By using the fundamental counting rule, the permutation rules, and the combination rule, you can compute the probability of outcomes of many experiments, such as getting a full house when 5 cards are dealt or selecting a committee of 3 women and 2 men from a club consisting of 10 women and 10 men. Bluman, Chapter 4

Chapter 4 Probability and Counting Rules Section 4-5 Example 4-50 Page #237 Bluman, Chapter 4

Four Aces Make problem simpler! Find the probability of drawing four aces when five cards are drawn from a deck of cards. Make problem simpler! Bluman, Chapter 4

Bluman, Chapter 4

𝑃 𝐴𝑐𝑒𝑠 = 4 𝑎𝑐𝑒𝑠 𝑎𝑛𝑑 𝑎𝑛𝑜𝑡ℎ𝑒𝑟 𝑐𝑎𝑟𝑑 𝑎𝑛𝑦 5 𝑐𝑎𝑟𝑑𝑠 𝑃 𝑎𝑐𝑒𝑠 = 4 𝑐 4∙ 48 𝑐 1 52 𝑐 5 = 1∙48 2,598,960 Bluman, Chapter 4

Final answer and rounding 1.84689∙ 10 −5 𝑂𝑅 0.0000184689 OR 0.000018 Bluman, Chapter 4

Four of a Kind Find the probability of getting four of a kind when five cards are drawn from a deck of cards. The answer to the last problem multiplied by 13; since there are 13 four of a kind hands possible. 𝟐.𝟒𝟎𝟎𝟗𝟔𝟎𝟑𝟖𝟒∙ 𝟏𝟎 −𝟒 =𝟎.𝟎𝟎𝟎𝟐𝟒 Bluman, Chapter 4

Chapter 4 Probability and Counting Rules Section 4-5 Example 4-51 Page #238 Bluman, Chapter 4

Example 4-51 A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities. A.) Exactly 2 are defective. B.) None is defective. C.) All are defective. D.) At least 1 is defective.

Example 4-52: Committee Selection A store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased. TV Graphic: One magazine of the 6 magazines Newstime: One magazine of the 8 magazines Total: Two magazines of the 14 magazines Bluman, Chapter 4

Chapter 4 Probability and Counting Rules Section 4-5 Example 4-52 Page #238 Bluman, Chapter 4

Chapter 4 Probability and Counting Rules Section 4-5 Example 4-53 Page #239 Bluman, Chapter 4

Example 4-53: Combination Locks A combination lock consists of the 26 letters of the alphabet. If a 3-letter combination is needed, find the probability that the combination will consist of the letters ABC in that order. The same letter can be used more than once. (Note: A combination lock is really a permutation lock.) There are 26·26·26 = 17,576 possible combinations. The letters ABC in order create one combination. Bluman, Chapter 4

On your own: Read “Speaking of Statistics” on page 240 Sec 4-5 page 240 Exercises #1-17 odds Bluman, Chapter 4