Worksheet titled "Basic Probability Worksheet" with problems involving marbles, dice rolls, and letters, including visual aids like a die, marbles, and a spinner.

Here are the step-by-step solutions for the problems on the worksheet.

Marbles

1. Probability of selecting a red marble
* Step 1: Count the total number of marbles in the bag.
$5 \text{ (red)} + 3 \text{ (blue)} + 2 \text{ (green)} = 10 \text{ total marbles}$.
* Step 2: Identify the number of "favorable" outcomes (red marbles). There are 5 red marbles.
* Step 3: Write the probability as a fraction: $\frac{\text{Red Marbles}}{\text{Total Marbles}}$.
$\frac{5}{10}$
* Step 4: Simplify the fraction. Both numbers can be divided by 5.
$\frac{1}{2}$

2. Probability of drawing a black marble then a gray marble (without replacement)
* Step 1: Find the total number of marbles initially.
$6 \text{ (white)} + 4 \text{ (black)} + 2 \text{ (gray)} = 12 \text{ total marbles}$.
* Step 2: Find the probability of the first draw (Black).
There are 4 black marbles out of 12.
$P(\text{Black}) = \frac{4}{12}$. This simplifies to $\frac{1}{3}$.
* Step 3: Adjust for the second draw. Since we did not replace the first marble, there is now one less marble in the bag ($12 - 1 = 11$ total). The number of gray marbles is still 2.
* Step 4: Find the probability of the second draw (Gray).
$P(\text{Gray}) = \frac{2}{11}$.
* Step 5: Multiply the probabilities together to find the chance of both happening.
$\frac{1}{3} \times \frac{2}{11} = \frac{1 \times 2}{3 \times 11} = \frac{2}{33}$.

3. Probability of selecting a blue marble
*(Note: The question text cuts off, but based on the pattern, it asks for the probability of selecting a specific color, likely blue).*
* Step 1: Count the total number of marbles.
$8 \text{ (red)} + 5 \text{ (blue)} + 3 \text{ (green)} = 16 \text{ total marbles}$.
* Step 2: Identify the number of blue marbles. There are 5.
* Step 3: Write the fraction.
$\frac{5}{16}$ (This cannot be simplified further).

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Dice Roll

A standard die has 6 sides numbered 1, 2, 3, 4, 5, and 6. The total number of possible outcomes is always 6.

a) Rolling a 5
* There is only one "5" on the die.
* Probability: $\frac{1}{6}$

b) Rolling an even number
* The even numbers on a die are: 2, 4, 6.
* There are 3 even numbers.
* Probability: $\frac{3}{6}$, which simplifies to $\frac{1}{2}$.

c) Rolling an odd number
* The odd numbers on a die are: 1, 3, 5.
* There are 3 odd numbers.
* Probability: $\frac{3}{6}$, which simplifies to $\frac{1}{2}$.

d) Rolling a prime number
* Prime numbers are numbers divisible only by 1 and themselves. On a die, these are: 2, 3, 5. (Note: 1 is not a prime number).
* There are 3 prime numbers.
* Probability: $\frac{3}{6}$, which simplifies to $\frac{1}{2}$.

e) Rolling a 2, 3, or 5
* We are looking for any of these three specific numbers.
* There are 3 favorable outcomes (2, 3, and 5).
* Probability: $\frac{3}{6}$, which simplifies to $\frac{1}{2}$.

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Letters

1. Word: ELEPHANT
First, let's count the letters.
Total letters: 8 (E, L, E, P, H, A, N, T)

a) The letter is a vowel
* The vowels in this word are: E, E, A.
* There are 3 vowels.
* Probability: $\frac{3}{8}$

b) The letter is a consonant
* The consonants are: L, P, H, N, T.
* There are 5 consonants.
* Probability: $\frac{5}{8}$

c) The letter is E
* The letter 'E' appears twice in the word.
* Probability: $\frac{2}{8}$, which simplifies to $\frac{1}{4}$.

2. Word: COMPUTER
*(The question is cut off, but usually asks for the probability of picking a specific type of letter, like a vowel or consonant. Here is the breakdown for the most common questions)*
* Total letters: 8 (C, O, M, P, U, T, E, R)
* Vowels (O, U, E): 3
* Consonants (C, M, P, T, R): 5
* *If asked for a vowel:* $\frac{3}{8}$
* *If asked for a consonant:* $\frac{5}{8}$

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Final Answer:

Marbles
1. $\frac{1}{2}$
2. $\frac{2}{33}$
3. $\frac{5}{16}$

Dice roll
a) $\frac{1}{6}$
b) $\frac{1}{2}$
c) $\frac{1}{2}$
d) $\frac{1}{2}$
e) $\frac{1}{2}$

Letters
1a) $\frac{3}{8}$
1b) $\frac{5}{8}$
1c) $\frac{1}{4}$
2) (Likely $\frac{3}{8}$ for vowel or $\frac{5}{8}$ for consonant)