Probability

Question 1

What is the definition of probability?

Answer 1

probability = want / total

Question 2

Using the probability formula, what is the chance when I flip a coin that it lands on heads?

Answer 2

probability = want = 1 / total = 2

Question 3

If you have all of the digits from 0 - 9 and you select one of them randomly, what is the probability that the digit is prime?

Answer 3

= 4 / 10

or as a percent = 40%

Question 4

All probability is expressed between 0 and 1 or 0 and 100%

Answer 4

If the probability is 0 or 0% it means it will never happen

If the probability is 1 or 100% it means it will happen

Question 5

Total number of outcomes that satisfy the requirements / total number of outcomes

Answer 5

probability

Question 6

Five men and six women are available to serve on a three-person committee. If the three members are chosen at random, what is the probability that the committee includes at least one woman?

Answer 6

When it says includes at least one woman, you can calculate the changes of getting no women and then subtract that number from 1.

So what are the chances that you get a committee with all men?
5 / 11 * 4 / 10 * 3 / 9 = 2 / 33
Then you need to subtract 2/33 from 1 to get your answer
so 1 - 2/33 = 31/33

Question 7

When you see the word “at least” what can you do?

Answer 7

You can calculate the event that is not occurring and subtract that answer from 1

Question 8

A candy jar contains 3 orange gumdrops and 4 lime gumdrops. If two gumdrops are randomly chosen from the jar, what is the probability that both an orange and a lime gum drop are selected?

Answer 8

Formula will be Probability of (Orange and Lime) = P(L,O) + P(O,L)
So,
Probability of (Orange and Lime) = (4/7 * 3/6) + (3/7 * 4/6)
So,
Probability of (Orange and Lime) = 2/7 + 2/7 = 4/7

Question 9

Griffin has a bag of marbles that contain only six black marbles and four red marbles. If he removes three marbles at random without replacing any of the marbles, what is the probability that all three marbles that will be selected are red?

Answer 9

Because he is going to pull out three different marbles write the sequence out
Note he doesn’t replace as he goes
Red Red Red
4/10 * 3/9 * 2/8 = 1/30
What is the probability of red and red and red ? You can multiply
Answer = 1/30

Question 10

The probability of an event occurring and the probability of an event not occurring always add up to what?

Answer 10

the probability of an event occurring and the probability of an event not occurring always add up to 1

Question 11

What should you do when you see AND probability?

Answer 11

Multiply

Question 12

Alejandro flips a coin four times. What is the probability that he gets heads on the first two throws and tails on the last two throws?

Answer 12

Answer = 1/16

.5 x .5 x .5 x.5 = .0625

Question 13

Probability doesn’t change from the previous probability, even if you got heads on a coin flip 10 times, on the 11th time its still a 1/2 probability.

Question 14

Probability of A and B = ?

Answer 14

Probability of A x Probability of B

multiply

Question 15

the term “both” can also mean what in a probability question?

Answer 15

“both” can also mean “and” in a probability question, in which case you multiply

Question 16

“or” probability (with mutually exclusive events)

ex. if I roll a dice I can roll a 2 or a 6 you can’t roll both

Answer 16

translate the word “or” into a +

addition

Question 17

Anne has a deck of 52 cards, each made up of four suits, each card numbered 1 through 13. If she selects a card at random, what is the probability that she selects a 2 or a 7 or a 9?

Answer 17

Because you have four suits, and each card is numbered 1 - 13 you have 4 twos, 4 sevens and 4 nines.

so,
4/52 + 4/52 + 4/52 = 12/52 which equals 3/13

Question 18

Probability of A or B = ?

Answer 18

Probability of A + Probability of B

Question 19

“at least” probability

The probability of rain on each of five days is 1/6, except on the first day, when it is 2/5 and on the last day when it is 4/5. What is the probability that rain will occur on at least one of the five days?

Answer 19

100% - No Rain = chance for some rain

Chances that there is no rain for each day:
M T W TH F
3/5 5/6 5/6 5/6 1/6

So multiply each of these things = 375/5,400

1 - 375/5,400 = .9305556

= 67/72

Question 20

“at least” probability

Answer 20

Find the probability that the event does not happen, and subtract it from 1.

Question 21

Probability of A = ?

Answer 21

Probability of A = 1 - Probability of Not A

Question 22

Four people are playing a game in which each person rolls a six sided die at the same time.

QA: 2/3

QB: The probability that at least two of the people roll the same number

Answer 22

Start by thinking that no one rolls the same number

1st person rolling what is the chance they will roll something no one else has rolled? = 6/6 (because they are going first)

2nd person: 5/6

3rd person: 4/6

4th person: 3/6

So,

6/6 x 5/6 x 4/6 x 3/6 = 5/18 (which is the likelihood that no one rolls the same number)

So 1 - 5/18 = 13/18

Since 13/18 > 2/3 the answer is B

Question 23

A bowl contains 4 red marbles and 12 blue marbles. If two marbles are selected at random one after the other without replacement, what is the probability that both a red and blue marble will be selected?

Answer 23

= 2/5

Question 24

If jake has a 1/3 chance of making his football team and a 1/6 chance of making the basketball team, what are the chances he makes both?

Answer 24

multiply!

1/3 * 1/6 = 1/18

answer = 1/18

Question 25

A certain jar contains only pennies and nickels in a ratio of 5 to 11, respectively. If Mike selects one coin at random from the jar, what is the probability that it will be a nickel?

Answer 25

Answer = 11/16

Remember that a ratio expresses a part to part relationship. While a fraction (which is what probability it) expresses a part to a whole relationship.

The whole in this case is the 16 total parts (5 + 11) you get from the ratio. The parts you are interested in (that is, the outcome you want) are the 11 nickels. Therefore the probability will be 11/16

Question 26

When a coin is dropped into a certain slot of a machine, it is dropped in 1 of 3 randomly selected bins. If 3 coins are dropped in the slot, what is the probability that all 3 coins are deposited in the same bin?

Answer 26

First coin can go into any bin, so out of the 3 bins so the probability of the first coin going into a bin is 3/3 or 1 (it will def go in a bin)

for the second coin, it now has to land in the bin the first coin landed in, so there is only one option for the second coin so that probability is 1/3

for the 3rd coin it has to land in the bin that the first and second coin are in and there is again, a 1/3 probability for that.

Now multiply the three separate events together to get 1/9 (1 * 1/3 * 1/3)

Question 27

When you see the word “at least” with probability what do you know you can do?

Answer 27

probability of at least 1 desired outcome = 1 - the probability that none of the desired outcomes happen

Question 28

U , V and W attempt to win a game. U and V each have a 1/4 chance of winning the game, W has a 1/3 chance of winning the game. What is the probability that at least one of the three wins the game?

Answer 28

REMEMBER - probability of at least 1 desired outcome = 1 - the probability that none of the desired outcomes happen

So the probability of V not winning is 3/4 (which is 1 - 1/4)
the probability of U not winning is 3/4
the probability of W not winning is 2/3

then multiply the probabilities of them not winning: 3/4 * 3/4 * 2/3 = 3/8 then subtract that from 1

so 1 - 3/8 = 5/8

answer = 5/8

Question 29

If a pair of fair, 6 sided dice, each with faces numbered one through six, is rolled, then what is the probability that the product of the two numbers facing up is even?

Answer 29

answer = 3/4

3/6 * 3/6 = 1/4

Now, the probability of an even product is the sum of the probabilities of the three - mutually exclusive (“or”) ways to get an even product: 1/4 + 1/4 + 1/4 = 3/4

e * e = e
e * o = e
o * e = e
o * o = o

Question 30

if two fair, six sided dice, each with faces numbered one through six, are rolled, then what is the probability that the sum of the two numbers facing up is neither 7 nor 8

Answer 30

there are 11 different ways to roll either a 7 or a 8
there are 6 * 6 total possible outcomes of rolling two six-sided die
therefore the probability of rolling a sum of 7 or 8 is 11/36 now you need to subtract this from 1 to get the answer
1 - 11/36 = 25/36

Question 31

If two fair, six sided dice, each with faces numbered one through six, are rolled, then what is the probability that the sum of the two numbers facing up is less than or equal to 10

Answer 31

there are only 3 cases that fit the exact opposite of the parameters in the question to be greater than 10: 5 + 6, 6 + 5, and 6 + 6

there are 6 * 6 possible outcomes for rolling two dice = 36

so 3/ 36

then you need to subtract that from 1

1 - 3/36 = 11 / 12

answer = 11 / 12

Question 32

to find the probability of two or more mutually-exclusive (OR) events, what do you do?

Answer 32

find the individual probability of each event, and add them together.

Question 33

A bag of candies contains only 6 peppermint flavored candies and 2 chocolate flavored candies. If there are no other candies in the bag, and two candies are randomly selected from the bag without replacement, then what is the probability that both candies are the same flavor?

Answer 33

to find the probability of two mutually exclusive (OR) events, find the individual probability of each event and add them together.

so you need to calculate:

P P = 6/8 * 5/7

and (+)

C C = 2/8 * 1/7

and when you do, answer = 1/28

Question 34

A fair, three sided die with sides numbered 1, 2 and 3 is rolled twice.

QA: The probability that the number 3 is rolled at least once

QB: 5/9

Answer 34

Because it is asking for the probability that the number 3 is rolled at least once first find the probability that the number 3 is never rolled for each of the 2 dice

dice 1 : probability that 3 is not rolled = 2/3
dice 2 : probability that 3 is not rolled = 2/3

not take those two, multiply and subtract the answer from 1

2/3 * 2/3 = 4/9

1 - 4/9 = 5/9 , answer = 5/9