SB probability and sample space.notebook
March 28, 2016
Probability
Sample Space
Theoretical Probability
An outcome is the result of a single observation or experiment.
P(E) = number of favorable outcomes
total number of possible outcomes
A die is tossed, what is the
probability of:
a) 3
b) even number
c) a number greater than 3
SB probability and sample space.notebook
March 28, 2016
Sample Space of an experiment is the set of all possible outcomes of the experiment. List the possible outcomes in the sample space:
1) flipping a coin
2) Rolling a die
3) Shooting a free throw in a basketball game
4) Tossing an empty can to see how it lands
Probability is a measure of how likely it is that an event will happen. 1. What is the probability of obtaining a
7 on a roll of a die?
2. What is the probability of obtaining
a 5 on a roll of a die?
3. What is the probability of obtaining a number
less than 7 on a roll of a die?
Probability of an event
0≤P(E)≤1
SB probability and sample space.notebook
March 28, 2016
A probability is a number between 0 and 1.
An event that is impossible has a probability of 0.
An event that is certain has a probabilty of 1.
What do you think it means for an event to have a probability of: a) 1/2
b) 1/4
c) 3/4
SB probability and sample space.notebook
March 28, 2016
Complement of an Event
(The complement of an event, A, denoted by Ac, is the event that A does not occur)
Ac = 1 ­ P(A)
A die is tossed, what is the
probability of:
a) not getting a 6
b) not an even number
c) a number less than 4
A gumball machine contains gumballs of five different colors:
36 red, 44 white, 15 blue, 20 green, and 5 orange.
The machine dispenser randomly selects one gumball. What is the probability that the gumball selected is:
a.) green?
b.) not green?
c.) not orange?
d.) orange?
e.) not a color in the flag of the USA?
f.) red, white, or blue?
SB probability and sample space.notebook
What is the probability of obtaining a head on a coin and a 6 on a die?
List the sample space:
Tree Diagrams can be used to organize outcomes in the sample space for chance experiments performed in multiple stages. March 28, 2016
SB probability and sample space.notebook
March 28, 2016
An experiment consists of flipping a nickel and a dime.
a) Draw a tree diagram or list the sample space.
b) Find 1)P(no tails)
2) P(1 tail)
3) P(1 or 2 tails)
An experiment consists of flipping a coin and rolling a die?
Find:
1) P(H,3)
2) P(T, 2 or 3)
3) P(H,Even)
4) P(T, 1 or 2 or 3)
5) P(H or T, 3)
SB probability and sample space.notebook
March 28, 2016
A family decides to play a game each night. They all agree to use a tetrahedral die (4 sided pyramidal die where each of the 4 outcomes are equally likely) each night to randomly determine if they will play a board game(B) or a card game(C).
For the family a card game will be played if the die lands showing a value of 1 and a board game will be played if the die lands showing a value of 2,3,or 4.
P(card game) =
P(Board game) =
Draw a tree diagram for Monday and Tuesday including the probabilities.
Two friends meet at a grocery store and remark that a neighboring family just welcomed their second child. It turns out that both children in this family are girls, and they are not twins. One of the friends is curious about what the chances are of having 2 girls in a family's first two births. Suppose that for each birth, the probability of a boy is 0.5 and the probability of a girl is 0.5.
1) Determine the probabilities for each of the 4 possible birth outcomes for a family with 2 children(no twins).
2) What is the probability of having 2 girls? Is that greater than or less than the probability of having exactly 1 girl in 2 births?
SB probability and sample space.notebook
March 28, 2016
Determine the probabilities for each of the 8 possible
birth outcomes for a family with 3 children(no twins or triplets).
What is the probability of a family having 3 girls? Is that greater than or less than the probability of having exactly 2 girls in 3 births?
What is the probability of a family of 3 children having a) atleast 1 girl?
b) atmost 1 girl?
Homework
SB probability and sample space.notebook
March 28, 2016