Independent Events: P(A and B) = P(A) · P(B)
Dependent Events: The probability of one event occurring depends
on the occurrence of another event. There are two types; with or without replacement
Ex 1: Suppose a hat contains 5 red and 3 blue tickets. One ticket is randomly chosen, its color is noted and it is thrown in a bin. A second ticket is randomly selected. What is the chance that it is red? Sample Space
a) If the first ticket was red, P(second is red) = ____________
b) If the first ticket was blue, P(second is red) = ___________
So, the probability of the second ticket being red DEPENDS on what color the first ticket was; however, the ticket was thrown back in the bin. Therefore, the denominator of the second event DOES NOT CHANGE! This is called probability WITH REPLACEMENT.
Ex 2: A box contains 4 red and 2 yellow tickets. Two tickets are randomly selected, one by one from the box and then returned to the box. Find the probability that:
Sample Space:
a) both are red ___________
b) the first is red and the second is yellow. ______________
You Do: You have a deck of cards, and you are going to pull three cards from the deck, replacing them each time. What is the probability that:
a) You pull three face cards ____________
b) You pull 3 aces _____________
c) You pull no face cards ______________ | |
|Dependent Events Without Replacement |
| |
|Example 1: Consider a box containing 3 red, 2 blue, and 1 yellow marble. If we draw two marbles out what is the probability of getting: |
| |
| |
| |
| |
| |
| |
| |
|two red marbles if replacement occurs: |
|two different colors if replacement occurs. |
| |
| |
| |
| |
| |
| |
| |
|two red marbles if replacement does not occur: |
|Two different colors if replacement does not occur. |
| |
|When doing probability WITHOUT REPLACEMENT the denominator of the 2nd event occurring must be reduced by one. The numerator of the second event |
|occurring must be reduced by one ONLY IF THE FIRST EVENT WAS THE SAME OUTCOME AS THE SECOND EVENT |
| |
|Ex 2: A hat contains 7 names of players in a tennis squad including the captain and the vice captain. If a team of 3 is chosen at random by drawing the|
|names from the hat, determine the probability that it does not: |
| |
| |
| |
|a) contain the captain _________ b) contain the captain or the vice captain ___________ |
| |
|You Do: 5 tickets numbered 1, 2, 3, 4, and 5 are placed in a bag. Two are taken from the bag without replacement. Determine the probability of |
|getting: |
| |
| |
| |
|both odd |
|both even |
|one odd and one even |
| |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.