WARM UP 1) JoJo and Kiki are visiting the Empire State Building. Each of them enters a different elevator in the main lobby that can let them off on any.

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WARM UP 1) JoJo and Kiki are visiting the Empire State Building. Each of them enters a different elevator in the main lobby that can let them off on any floor from 1 to 3. Assuming that they are as likely to get off at one floor as another, what is the probability that they both get off on the same floor? 2) A family plans to have 2 children. What is the probability that both children will be girls? 3) What is the probability of getting a black jack?

HOMEWORK 4) a) 126/316 b) 5/316 c) 8/316 8) 4 drunks, 4 Jackets 10) 3 patients, 3 samples 12) 10,000 microwaves, recalled ones with last digit of 5, 6, or 7

Section 4.3 Counting Rule An easy way to find total possibilities or the SAMPLE SPACE

Counting Rule MULTIPLY

LICENSE PLATES In Delaware, license plates have seven characters. How many possibilities are there total? What if you could only use numbers? What if you could only use letters? What if you can’t repeat letters? What if you do not have any restrictions at all? 10·10·10·10·10·10·10= 10,000,000 26·26·26·26·26·26·26= 8,031,810,176 26·25·24·23·22·21·20= 3,315,312,000 36·36·36·36·36·36·36= E 10

PASSWORDS Most internet sites force you to have a password. If one site requires 8 characters, letters only, how many possibilities are there? 26·26·26·26·26·26·26·26= E 11

CELL PHONES How many phone numbers are possible in Delaware? Are there enough possibilities if everyone had their own cell phone? (There are about 850,000 people living in Delaware) 1·1·1·8·10·10·10·10·10·10= 8,000,000 (302)…-….

DIGITS How many five digit numbers can be formed from the digits 2, 4, 5, 6, 7 if the number must be bigger than 50,000 without repetition? If we allowed repetition, how many possibilities are there? __ · __ · __ · __ · __ 3·4·3·2·1= 72 ways3·5·5·5·5= 1,875 ways __ · __ · __ · __ · __