Probability

Theoretical/Experimental

100

What is Experimental probability

Experimental probability is the chances of an event happening based on results.

200

What is the probability of flipping a coin three times and getting 3 tails in a row?

P(tail)xP(tail)xP(tail) = (.5)x(.5)x(.5) = .125 = 1/8

300

Allison rolled a die 25 times and it landed on the number 3 5 times. What is her experimental probability of landing on the number 3?

What is 5/25 = 1/5

400

A bag contains 7 onion bagels, 9 sesame bagels and 11 plain bagels. If someone picks a random bagel what is the probability that it will NOT be a sesame bagel?

What is P(onion) + P(plain) = 7/27 + 11/27 = 18/27

500

Adam has 2 nickels, 1 dime and 2 quarters in his pocket. he takes out a single coin at random. what is the probability that the coin he picks is less than $0.25?

What is P(nickel) + P(dime) = 2/5 + 1/5 = 3/5

Miscellaneous

100

What is the probability of an event is equally likely?

1/2

200

What is the probability of rolling an even number on a six sided die?

P(even) = 3/6 = 1/2

300

What is the sample space of flipping a coin two times in a row?

Sample Space: { HH, HT, TH, TT }

400

What are exclusive events?

Mutually exclusive events are events that cannot happen at the same time. Ex. when flipping a coin, cannot land on both heads and tails.

500

I am buying two gumballs from a machine with 3 blue, 10 yellow, 8 red, and 4 orange gumballs. What is the P(picking blue or yellow)?

P(blue or yellow) = P(blue) + P(yellow) = 3/25 + 10/25 = 13/25

Permutations

100

What makes permutation different than the counting principle?

When using permutations, the order in which the objects are arranged matters.

200

What is the permutation notation for choosing 5 students from 10 students?

What is choosing 5 students from 10 students = 10P5

300

There are 11 students to choose from to play soccer. We want to choose 3 students to play different positions. How would you write the permutation notation for this problem?

Choosing 3 students out of 11 = 11P3

400

There are 11 students to choose from to play soccer. We want to choose 3 students to play different positions. Why does this problem use permutations?

This uses permutations because the positions in which the students play are different, so the order in which they are chosen to play each position matters.

500

There are 11 students to choose from to play soccer. We want to choose 3 students to play different positions. Now calculate the different ways we can choose 3 students for different positions out of 11 students.

11p3 = 11 x 10 x 9 = 990 different ways to choose 3 students from 11

Independent/Dependent Events

100

What are two events that do not affect each other?

Two events that do not affect each other are dependent events.

200

You like to eat popcorn and you studied a lot for Ms. Rafti's test. Are these events dependent or independent? Why?

These events are independent because knowing that you like popcorn does not tell me anything about the probability that you studied for Ms. Rafti's test.

300

A deck of cards has 3 blue, 4 black, and 6 purple cards. You pick 2 cards from the deck. Cards are not returned to the deck after they are picked. P(two blue cards in a row)

P(two blues in a row) = (3/13)x(2/12) = 6/156 = 1/26

400

I am choosing from a bag of marbles with 2 pink, 3 apricot, 6 lavender, and 4 seafoam marbles. The marbles are put back because I do not want to lose them. What is the P(pink, then lavender)?

P(pink, then lavender) = P(pink) x P(lavender, after picking pink) = 2/15 x 6/15 = 12/225

500

I am buying two gumballs from a machine with 3 blue, 10 yellow, 8 red, and 4 orange gumballs. Of course, after I receive a gumball, I cannot put it back into the machine. What is the P(red, then white)?

P(red, then white) = P(red) x P(red, then white) = 8/25 x 0 = 0

Counting Principle

100

What can we draw to help us find all of the different possibilities of an event?

What is a tree diagram

200

2 pens (red or green) and there 6 pencils (silver,purple,gold,orange,black, and brown) How many possible outcomes?

What is 12

300

There are 6 cars (chevy, nissan, toyota, BMW, bently and GMC) and there are 3 locations you can go with each car (utah, colorado and florida). How many possible outcomes are there?

What is 6 cars x 3 locations = 18 different possible outcomes

400

2 pens (red or green) and there 6 pencils (silver,purple,gold,orange,black, and brown) How many outcomes include a green pen?

1/2 of the options include a green pen

500

At a sub shop, we can pick from three meats: Ham, Turkey, or Salami. We can pick from two toppings: lettuce or tomato. And there are 2 different dressings we can use: Honey mustard or mayonnaise. How many different sandwiches can we make using 1 meat, 1 topping, and 1 dressing?

What is 3 meats x 2 toppings x 2 dressings = 12 different sandwiches