50+ Probability of Compound Events worksheets for 6th Grade on ... - Free Printable

Here are the step-by-step solutions for the problems shown in your worksheet.

Question 1

Problem: Ricardo has a spinner (divided into 4 equal sections: red, yellow, blue, green) and a bag with 2 red, 3 green, and 3 blue marbles. What is the probability that he spins red AND picks a red marble?

Step 1: Find the probability of spinning red.
The spinner has 4 equal sections. Only 1 section is red.
$$ P(\text{Spin Red}) = \frac{1}{4} $$

Step 2: Find the probability of picking a red marble.
First, count the total number of marbles: $2 \text{ (red)} + 3 \text{ (green)} + 3 \text{ (blue)} = 8$ total marbles.
There are 2 red marbles.
$$ P(\text{Pick Red}) = \frac{2}{8} $$
(This simplifies to $\frac{1}{4}$, but we can keep it as $\frac{2}{8}$ for now).

Step 3: Multiply the probabilities.
Since these are independent events (the spinner doesn't affect the bag), you multiply the two fractions together:
$$ \frac{1}{4} \times \frac{2}{8} = \frac{2}{32} $$

Step 4: Simplify.
Divide the top and bottom by 2:
$$ \frac{2 \div 2}{32 \div 2} = \frac{1}{16} $$

Correct Option: D

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Question 2

Problem: How many outcomes are there with tossing a coin and rolling a dice?

Step 1: Count the outcomes for the coin.
A coin has 2 sides: Heads and Tails.
Outcomes = 2

Step 2: Count the outcomes for the dice.
A standard dice has 6 numbers: 1, 2, 3, 4, 5, 6.
Outcomes = 6

Step 3: Multiply to find total combinations.
To find the total number of unique pairs (like "Heads and 1", "Tails and 5"), you multiply the possibilities:
$$ 2 \times 6 = 12 $$

Correct Option: D

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Question 3

Problem: What is the probability of picking a blue marble, putting it back in the bag, then picking a red marble?

*Note: Looking at the bag in the image, let's count the marbles carefully.*
There are 4 Blue marbles and 3 Red marbles.
Total marbles = $4 + 3 = 7$.

Step 1: Probability of the first pick (Blue).
There are 4 blue marbles out of 7 total.
$$ P(\text{Blue}) = \frac{4}{7} $$

Step 2: Account for "Putting it back".
Because you put the marble back, the total number of marbles stays at 7 for the second turn. This is called "probability with replacement."

Step 3: Probability of the second pick (Red).
There are 3 red marbles out of 7 total.
$$ P(\text{Red}) = \frac{3}{7} $$

Step 4: Combine them.
You multiply the two probabilities:
$$ \frac{4}{7} \times \frac{3}{7} $$

Correct Option: C

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Question 4

Problem: If you spin two times, what is the probability of landing on green both times?

Step 1: Analyze the spinner.
The spinner is divided into 6 equal slices.
Count the colors:
- Red: 2 slices
- Blue: 2 slices
- Yellow: 1 slice
- Green: 1 slice

Total slices = 6.

Step 2: Probability of landing on Green once.
There is 1 green slice out of 6.
$$ P(\text{Green}) = \frac{1}{6} $$

Step 3: Probability of landing on Green twice.
Since you are spinning again, the odds stay the same. You multiply the probability by itself:
$$ \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} $$

*(Note: The options for this question were cut off in the image, but based on the math, the answer is 1/36).*

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Final Answer:
1. D (1/16)
2. D (12)
3. C (4/7 x 3/7)
4. 1/36