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Vocabulary
Simulations
Complimentary Events
Common Misconceptions
What is the Probability?
100

Probability based on past results or a simulation.

Ex. If you flip a coin 5 times and get heads 3 times, P(heads) = 3/5

 

What is experimental probability?
100
About 5% of students in the US have ADHD.  This is how you would represent students with ADHD using the numbers 00-99.
What is 00,01,02,03,04 or any other five numbers?
100
Rolling an even number
What is complimentary to rolling an odd number?
100

Simone has been flipping a coin and has just flipped 5 heads in a row. She says that because she has just gotten so many heads, she is more likely to get tails than heads the next time she flips.  This is the concept that Simone doesn't understand.

What is dependent and independent events?  Flipping a coin is not dependent on previous flips. Each time she flips she is equally likely to get heads or tails.  Also, the experimental probability may not equal the theoretical probability.  It should get closer to the theoretical probability with a large number of trials.  (The Law of Large Numbers)


100
If you roll two dice, the theoretical probability of getting a sum of 4 is this fraction.
What is 3/36 or 1/12?
200
The expected probability based on calculations, or the number of possibilities and likelihood of each possibility.

P(heads) = 1/2

What is theoretical probability?
200

About 5% of students in the US have ADHD. This is how many numbers you would select if you wanted to approximate the probability of having 3 or more students with ADHD in a class of 20 students.

What is 20 numbers?
200
Getting at least 1 odd number in 3 rolls
What is complimentary to not getting any odd numbers in 3 rolls?
200

The probability of winning a game is 3/1000. Andre say this means that if you play this game 1000 times, you will win 3 times.  3/1000 is this type of probability.

What is the theoretical probability?

A probability of 3/1000 does not necessarily mean that you will win 3 of every 1000 games.  What happens when you play the game is the experimental probability, and the theoretical probability is the likelihood of your winning.

200
If you roll two dice, the probability of rolling an even number on both dice is this fraction.
What is 1/4?

1/2 x 1/2

EE; OO; EO; OE

300
The favorable to unfavorable possibilities; written as a ratio


Getting a sum of 7 when rolling 2 dice = 6:30 or 1/5

What are odds?
300

About 5% of students in the US have ADHD. You would represent students with ADHD using the numbers 00-04 and students without ADHD with the numbers 05-99. You want to approximate the probability of having 3 or more students with ADHD in a class of 20 students.  This is what a successful trial would look like.

What is 20 numbers between 00-99 that may repeat and at least 3 numbers would be between 00-04?
300
Rolling a sum less than 8 on two dice.
What is complimentary to rolling a sum greater than or equal to 8 on two dice?
300

There are two bags, each containing red blocks and yellow blocks. Bag 1 contains 1 red block and 3 yellow blocks. Bag 2 contains 3 red blocks and 12 yellow blocks. Trevor says he is more likely to pick a red block out of bag 2 than bag 1 because bag 2 has more red blocks than bag 1.  Trevor doesn't understand this about probability.

What is the number of possible success/number of possibilities if each outcome is equally likely?

Bag 1 P(red) = 1/4

Bag 2 P(red) = 3/15 = 1/5

It is true that there are more red blocks in bag 2, but there are also more yellow blocks.  The ratio of red to total blocks is greater in bag 1.

300
The probability that your team wins the coin flip 3 games in a row is this fraction.
What is 1/8?


1/2 x 1/2 x 1/2 = 1/8

400
Two events that do not overlap; no element can be in both groups.

Freshmen and Juniors

What are mutually exclusive events?
400

About 5% of students in the US have ADHD. You would represent students with ADHD using the numbers 00-04 and students without ADHD with the numbers 05-99. You want to approximate the probability of having 3 or more students with ADHD in a class of 20 students. 

00;35;23;14;36;26;88;66;54;32 22;79;84;93;02;44;61;29;06;18

This is the number of students in this class that would have ADHD.

What is two students?  This particular trial would be a failure because it doesn't have 3 or more numbers between 00-04
400
The probability of not rolling a sum of 11 or more when rolling two dice is this fraction. 
What is 33/36 or 11/12?

1- (3/36) 

5,6; 6,5; 6,6

400

Alex has a bag that is filled with 2 red balls and 1 white ball. Alex says that because there are two different colors he could pick from the bag, the probability of picking the red ball is ½.  There are actually this many outcomes in this situation.

What are 3 outcomes?

If you consider the color of balls, the probability of red is not the same as the probability of white because there are more red balls than white.

400

If 5 regular jelly beans and 5 bad tasting Harry Potter jelly beans are mixed in a bag, the probability of eating 3 jelly beans and not getting a bad one is this fraction.  

What is 1/12?

5/10 x 4/9 x 3/8 = 60/720 = 1/12

500
Two events that are mutually exclusive and include all possible outcomes; the combined probability = 1.

Getting a hit and not getting a hit

What are complimentary events?
500
A medical test is 80% likely to be accurate.  How might you set up a simulation to approximate the likelihood of the test being inaccurate for at least one patient if 5 patients are tested? How might you find the theoretical probability to the nearest tenth of a percent?
What is you might use the numbers 0-9 and select 8 of them to represent an accurate test?  Ex. 0-7 represent accurate test; 8 and 9 represent a false test.  Then you would select 5 numbers if all of them are between 0-7 it is a failure.  Otherwise it is a success.

Theoretical probability = 1 - (.8)^5 = .32768 = about 32.8%

500

If you roll two dice four times, the probability that you roll doubles at least once is this this percent that is rounded to the nearest tenth.

What is 51.8%

Compliment - no doubles - 6 sets of doubles out of 36 options 

1 - (30/36 x 30/36 x 30/36 x 30/36) = 1- 5/6 ^4

500

If you flip 2 coins simultaneously, there are 3 possible outcomes: both are heads, both are tails, or one is heads and one is tails. Anita asks if this means that the probability of getting one head and one tail is 1/3.  Anita doesn't understand this.

What is that there are 4 possible outcomes because there are two ways you could get one head and one tail?  Heads of right and tails on left; or tails on right and heads on left.  You could also draw a tree diagram to illustrate this.
500

If you have a package of M&Ms with 4 red and 3 yellow M&Ms, the probability that you pull out and eat 2 red M&Ms in a row is this fraction. 

What is 2/7?


4/7 x 3/6 = 12/42 or 2/7