Vocabulary
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
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)
P(heads) = 1/2
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.
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.
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.
1/2 x 1/2
EE; OO; EO; OE
Getting a sum of 7 when rolling 2 dice = 6:30 or 1/5
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.
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.
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.
1/2 x 1/2 x 1/2 = 1/8
Freshmen and Juniors
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.
1- (3/36)
5,6; 6,5; 6,6
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.
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.
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
Getting a hit and not getting a hit
Theoretical probability = 1 - (.8)^5 = .32768 = about 32.8%
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
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.
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.
4/7 x 3/6 = 12/42 or 2/7