Transcript PowerPoint

What is the probability of the following:
1.
2.
3.
Rolling a 4 on a die
Rolling an even number on a die
Rolling a number greater than 2 on a die
Answer the following:
4.
5.
*
*
Probability of Compound Events
*
1.
2.
Students play in pairs and take turns.
3.
Player 1 can continue as long as desired or
until the sum of the number cubes is
eight. If the sum is eight, the player loses
all points for that round. If the player
stops before getting a sum of eight, the
players record the total of all points for
the round.
4.
5.
Player 2 does the same.
6.
The player with the most points at the
end wins!
After rolling the number cubes, Player 1
records the sum of the numbers.
Both players use the chart to keep a
running total of points.
*
* Review: A Simple Event has only one outcome.
* New Info: A Compound Event is a combination of at
least two simple events.
* There are two kinds of compound events:
1. Independent Events - When the outcome of the first
event has no influence on the likelihood of a future
event occurring.
2.
Dependent Events - When the outcome of the first
event reduces the amount of possible outcomes (and
as a result, the likelihood) of future event(s).
*
What is the probability of rolling less
than a 5?
*
* To determine the probability of a compound event,
multiply the probabilities of the individual events.
Example: What is the probability of drawing a Queen and then a
King? There are 52 cards in a deck and in it are 4 Queens as well
as 4 Kings. So the odds are 4/52 (simplified to 1/13)
*1/13 = 0.063
*(about six
This one is
less than
1/10…
hundredths)
of this one!
*
*1/169 = 0.0059
*(about six
thousandths)
*
* A fair spinner is one on which all the
sections are the same size.
* A fair competition is one in which everyone
has the same probability of winning.
* To win, you must first spin a number higher than 7, and
then then spin an even number.
* Your probability
…
*
* Abbreviations are used to illustrate what happens when
we solve probabilities.
P: Means total probability
A: Refers to the first event
B: Refers to the second event
* Probability that 2 independent events will take place:
P(A&B) = P(A)P(B)
The probability of A and B both happening equals the
probability of A times the probability of B.
* Probability that 2 dependent events will take place:
P(A&B) + P(A)P (B following A)
The probability of A & B happening equals the probability
of A times the probability of B after A has happened.
*
* “Example: You share your last jelly beans with a friend.
* There are 12 jelly beans left over.
* Both of you like the red beans most. There are only 2.
* Your friend is next get to take two beans.
* What is the probability that she can get both red beans?
Note the pattern: P(A&B) = P(A)P(B following A)
*
* There are 12 marbles in the bag:
 2 Blue
 3 Yellow
 3 Green
 4 Red
* Your friend is to reach in and try to take out a yellow
marble. He will keep it out. You will try to the same
with a red marble. What is the probability of success?
*
* You will pick out three numbers between 1 and 30.
* You may only use a number once.
* If you pick the three winning numbers I have preselected, you will win the Grand Prize.
* But, in order to submit your numbers and compete, you
must also determine in writing the probability of
winning.
* You have 3 minutes to choose your numbers and figure
out the probability.
Do Not Click Again
until ready to reveal probability
*