Experimental or Theoretical
If I have to use collected data to know my probability, I am working with...
Experimental Probability
*It is EP as you are using the data (results) to get the probability after completing the experiment.
Flipping heads on a coin is an example of a...
Simple Event
*only 1 event is a simple event; you find the probability and you are done (e.g. P heads on a coin: 1/2 as there is 1 head and two outcomes on a coin: heads and tails)
There are 52 cards in a regular playing card deck. The probability of drawing the only Ace of Spades is...
1/52
*1 Ace of Spades (desired outcome)/total of 52 cards in a deck (total outcomes) = 1/52 chance
If you play as imposter on 20% of Among Us games, how many times can you expect to play imposter on 10 games?
2
*20% you are an imposter is + 20/100 meaning if you play 100 times, you'd be an imposter 20 times. So if you set up a proportion 20/100 = ?/10 you'd divide top and bottom by 10 getting 2/10 times. So 2 times you'd be the imposter if you only played 10 times.
A donut shop sells 3 kinds of juice and 5 kinds of donuts. How many ways can you buy one juice and one donut?
15 way
*you can make a tree diagram OR you can think 3 outcomes for juice x 5 outcomes for donuts = 15 total ways
If I know all of my outcomes are equally likely (rolling a die, drawing a card), then I am working with...
Theoretical Probability
*you can use the desired outcome out of the total outcomes to FIND/Predict what should happen (Theoretical Probability)
Drawing 2 aces in a hand of 5 is an example of a...
Compound Event
*It's a compound event (a.k.a multiple events) as you are doing more than 1 thing. You are trying to find P drawing in Ace from 5 cards and than P drawing another Ace from the cards. Once you find both you MULTIPLY the probabilities as you are trying to find the probability of MULTIPLE events.
The probability of rolling an even number on a 6-sided die is...
3/6 or 1/2
*1/2 the numbers are even on a die: 2, 4 and 6 so the probability is 1/2 OR 3 (# of even numbers on a die)/6 (total #'s on a die), so, 3/6 which, when simplified is 1/2.
1 out of 3 customers upgrade their combos to a large. How many combos will be upgraded if the restaurant sees 300 customers?
100
*1/3 upgrade then I'd make a proportion 1/3=?/300. I'd multiply by 100 upstairs and downstairs, so I'd get 100 customers out of 300 would be upgraded.
A bag has a red chip, blue chip, yellow chip, and green chip. What is the probability of drawing a red chip, replacing it, and then a blue chip?
1/16
*The P red and blue is:
P red is 1/4 then you put it back
P blue chip is not 1/4
Multiply events: multiply 1/4 x 1/4 = 1/16
Theoretical Probability tells me that the probability of flipping a heads is...
1/2
*There is 1 heads (desired outcome) which is your numerator/2 total outcomes on coin (heads & tails) which is your denominator.
Your friend puts one extra spicy chip in a bag with a bunch of normal chips. Getting the spicy chip on the first chip you eat is an example of a...
Simple Event
**only 1 event is a simple event; you find the probability and you are done
What is the probability of rolling a 7 on two dice?
0/36 = 0; it's impossible
*0 sevens on a die/6 numbers x 0 sevens on a die/6 numbers = 0/36 = 0% chance
10 students in a 7th grade class of 20 are making a B or better. How many students are making a B or better among all 300 7th graders?
150
*10/20 are making a B, that is the same as 1/2 that are making a B. So if there are 300 7th graders, 1/2 of them would be 150.
A bag has a red chip, blue chip, yellow chip, and green chip. What is the probability of drawing a red chip, replacing it, and then a blue chip?
1/12
*The P red and blue is:
P red is 1/4 then you keep it so there is only a blue, yellow and green still there.
P blue chip is now 1/3 (remember the red chip is gone so you are down a chip)
Multiply events: multiply 1/4 x 1/3= 1/12
Jimmy flips a coin 10 times and gets 3 heads. Experimental Probability tells me the probability of getting a heads on the next flip is...
3/10
*You used Experimental Probability (past results) to determine the future ones based on your experiment results.
Getting the winning lottery numbers is an example of a...
Compound Event
*
Compound Event
*It's a compound event (a.k.a multiple events) as there are SEVERAL numbers on a lottery ticket. You are trying to find P of each number in its position and then multiply ALL those probabilities together as it is MULTIPLE events (since the ticket has more than 1 number). This is why you have a 5 times better chance of being struck by lightning than winning the lottery.
Half of the cards in a deck of 52 playing cards are red and the other half are black. You draw a red card (keep it) and then draw a second card. What is the probability that the second card is also red?
25/102
*Probability of red and red (w/o replacement) 1/2 (cards are red) x 25/51 (assuming a red was drawn the 1st time) = 25/102.
A restaurant sells three kinds of sandwiches: Bacon, sausage, and ham. If 20% of sandwiches sold are bacon sandwiches, how many bacon sandwiches are sold out of 150?
30
*If 20% = 20/100 are bacon sandwiches, I'd make a proportion of 20/100 = ?/150. I multiply top and bottom by 1.5 so that would be 20 x 1.5 = 30 sandwiches with bacon.
What are the odds of rolling a number divisible by 5 on a pair of dice?
1/36
***5 is the only number divisible by 5 (and here is only 1 five on EACH die)so there is a 1/6 chance on one die and 1/6 chance on another die. When you multiply these MULTIPLE events you get:
1/6 x 1/6 = 1/36 so the answer is 1/36 chance
If the sections of a spinner are all different sizes, I must use ______ to find the probability of any outcome.
Experimental Probability
*It's hard to predict Theoretical Probability of a spinner if they are all different sizes.
Spinning a spinner and rolling a die is an example of a Simple or Compound Event?
Compound Event
Compound Event
*It's a compound event (a.k.a multiple events) as you are doing more than 1 thing. Once you find both you MULTIPLY the probabilities as you are trying to find the probability of MULTIPLE events.
What is the chance of drawing the Jack of Diamonds followed by another Jack of Diamonds from a full set of 52 cards?
0
*There is ONLY 1 Jack of Diamonds so if you find P of J of diam AND J of diam, it is impossible as you can't draw it again. Mathematically that's 1/52 x 0/51 = 0/2,652 = 0
A class of 15 has 5 kids who wear glasses. If the school has 600 students, how may of those students DON'T need glasses?
400
*So, if 5/15 WEAR glasses then 10/15 don't wear glasses. If there is 600 students, I'd set up a proportion and solve it. 10/15 x ?/600 = I'd multiply by upstairs and downstairs by 40 and get 440/600 who DON'T need glasses.
What are two ways to FIND all possible outcomes of a situation.
Make a tree diagram (like we did in class) and fundamental counting principle (multiple the number of outcomes together)
*Probability of spinning on a spinner with 10 equivalent (10 outcomes) colors and flipping tails on a coin (2 outcomes) so 10 x 2 is 20 outcomes. This is fundamental counting principle.