Question

Match the given situations with their correct probabilities. Answer should be expressed as fractions in a simplest form.

Answer 1

Hello! Let's analyze each exercise and solve it.

a. 1 spade from a standard deck:

$\frac{\text{cards of spade}}{\text{standard deck cards}}=\frac{13\text{ possibilities}}{52\text{ cards}}=\frac{13}{52}=\frac{1}{4}$

b. pick an ace or a two in a standard deck:

$\frac{\text{ number of A cards + number of 2 cards}}{\text{ standard deck cards}}=\frac{4+4}{52}=\frac{8}{52}=\frac{2}{13}$

c. Rolling the dice, what's the probability of getting a sum of 8 or more:

Let's write all possible results:

1,1; 1,2; 1,3; 1,4; 1,5; 1,6; ... ; 6,5; 6,6.

We have 36 possibilities of results.

Now, let's write just the possibilities that we want (sum of 8 or more):

2 + 6

3 + 5

3 + 6

4 + 4

4 + 5

4 + 6

5 + 3

5 + 4

5 + 5

5 + 6

6 + 2

6 + 3

6 + 4

6 + 5

6 + 6

So, we have 15 possibilities to get a sum of 8 or bigger, in a total of 36 possibilities:

$\frac{\text{ sum of 8 or bigger}}{total\text{ of possibilities}}=\frac{15}{36}=\frac{5}{12}$

d. 2 blue, 5 yellow, and 3 white marbles. What's the probability of pulling a blue marble from the bag?

Let's write the total of marbles: 2 + 5 + 3 = 10

$\frac{\text{blue marbles}}{\text{ total of marbles}}=\frac{2}{10}=\frac{1}{5}$