7-4 - Chapter 7.4: Counting Techniques and Probability In...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 7.4: Counting Techniques and Probability In many probability problems, the sample space S is too large to count simply by listing all sample points. If this is the case, we may use our different counting techniques (i.e. permutations, combinations, etc.) to find n ( S ) and n ( E ). Example: In the lottery BC-49, a player selects six different numbers from 1 , 2 , 3 , . . . , 49. On the day of the lottery drawing, the lottery official randomly selects the six winning numbers. If the player has exactly three of these numbers, then the player wins a $10 prize. What is the probability of a player winning the $10 prize with exactly one ticket? Let E be the event that exactly three numbers match. We need to count n ( S ) and n ( E ). First, the sample space consists of all possible selections of six numbers. The total number of ways in which 6 numbers can be selected from 49 is parenleftbigg 49 6 parenrightbigg . Thus, n ( S ) = parenleftbigg 49 6 parenrightbigg . To count n ( E ), there are two tasks: selecting three of the six winning numbers (which can be done parenleftbigg 6 3 parenrightbigg ways) and selecting three of the 43 remaining non-winning numbers (which can be done parenleftbigg 43 3 parenrightbigg ways). Thus, n ( E ) = parenleftbigg 6 3 parenrightbiggparenleftbigg 43 3 parenrightbigg . This gives us: P ( E ) = n ( E ) n ( S ) = parenleftbigg 6 3 parenrightbiggparenleftbigg 43 3 parenrightbigg parenleftbigg 49 6 parenrightbigg . 0176 The probability of winning the $10 prize is approximately 0.0176. Example: If all six numbers match, then the player wins the grand prize (usually at least $1 000 000). What is the probability that a player wins the grand prize with one ticket? Let E be the event that all six numbers match on the ticket. 1 Since the experiment has not changed, the sample space is the same, and n ( S ) = parenleftbigg 49 6 parenrightbigg ....
View Full Document

This note was uploaded on 02/05/2011 for the course MATH 377 taught by Professor Stephenlang during the Spring '11 term at University of Victoria.

Page1 / 5

7-4 - Chapter 7.4: Counting Techniques and Probability In...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online