Statistics - PSAT Math

Let be the total number of marbles in the box. Since there's a 10% chance of drawing a red marble, then implies there are 20 marbles total in the box. Thus, there are only 11 green marbles, resulting in the probability of drawing a green marble being

In order for the sum to be 3, the two rolls must be 1 and 2. However, it doesn't matter which one comes first. Therefore, there are 2 ways we can acquire the sum being 3. The total number of combination of two die is .

Thus, the probability of rolling a sum of 3 is .

The question is asking for the probability of drawing a 4 AND a Heart.

Prob(draw a 4) .

Prob(draw a Heart) .

Then the Prob(4 AND Heart) = Prob(4) * Prob(Heart)

You can also solve this question using logic instead of the rules of probability. We know there is only one four of hearts in a deck of cards, so the probability of drawing one must be .

Order matters, so a permutation of 15 things chosen 4 at a time, or , is the correct answer.

Adding the green, blue, and black marbles together gives 40. Then if there is a chance that a red marble is drawn, there must be an additional 20 marbles.

The chance she picks an apple is the total number of apples over the total number of fruits in the bowl. Since there are 2 kinds of apples, we add 2 red delicious and 3 granny smiths to get 5 apples total. In addition there are 4 more peices of fruit, so the total number of fruits is 9.

There is a total of 14 marbles, of which, 8 are yellow; therefore the probability of choosing a yellow marble is or

Because a yellow marble was selected and not replaced, there is a total of 13 marbles in the bag and of which, 7 are yellow; therefore, the probability of selecting a yellow marble is

The total number of possibiliities is 16. The outcome we are looking for is three girls and one boy which happens only four times. Thus the probability becomes .

The sample space for three coin tosses in a row is 8. Getting all heads can be done only one way. Getting all tails can be done only one way. So the probability of getting all heads or all tails is or .

The sample space for three children is 8. We can count up what we want or subtract out what we don't want. What we don't want is all boys or all girls.

So the probability becomes

Order matters, so we use permutations. is

Choosing one of each clothing item is an independent event and should be multiplied together. So the answer becomes

or

different combinations.

The probabilities of each pick changes as fewer marbles remain in the bag. Each selection order of the colors will yield the same probability, expressed as:

There are 16 different ways to flip a fair coin four times in a row. There is only one way to get all tails.

so the

The sample space for rolling two six-sided dice is 36.

Counting the wanted outcomes gives:

2: 1,1 (1)

3: 1,2 and 2,1 (2)

4: 1,3 and 2,2 and 3,1 (3)

5: 1,4 and 2,3 and 3,2 and 4,1 (4)

So there are 10 ways to get a five or less.

Thus the probability of getting a five or less is .

Order matters, so we use permutations: = .

Half of the scrunchies are black, so

One third of the scrunchies are white

One ninth of the scrunchies are blue

And the rest are green:

If we have already drawn two, our total amount of scrunchies is now 88, so the probability of pulling a black scrunchie will be:

of the students are wearing red shirts, and

One third of the students are wearing pink shirts

The remaining students are wearing orange

The probability of randomly selecting a student wearing an orange shirt is