Here are the step-by-step solutions for the problems shown in your worksheet.
1. Coin Toss and Spinner
*
Step 1: Find the probability of getting Heads on the coin. A coin has 2 sides (Heads and Tails), so the chance is $1/2$.
*
Step 2: Find the probability of landing on Red on the spinner. The spinner has 6 equal sections, and 2 of them are Red. So, the chance is $2/6$, which simplifies to $1/3$.
*
Step 3: Multiply the probabilities together because you need *both* things to happen.
$$ \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} $$
2. Car Combinations
*
Step 1: Count the choices for each category.
* Body styles: 2 doors, 4 doors, convertible =
3 options.
* Exterior colors =
3 options.
* Interior colors =
2 options.
*
Step 2: Multiply all the options together to find the total combinations.
$$ 3 \times 3 \times 2 = 18 $$
3. Rolling Two Dice
*
Step 1: Find the total number of possible outcomes. Each die has 6 sides, so $6 \times 6 = 36$ total outcomes.
*
Step 2: List the outcomes where the numbers are the same (doubles): (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). There are
6 matching pairs.
*
Step 3: Write the probability as a fraction and simplify.
$$ \frac{6}{36} = \frac{1}{6} $$
4. M & Ms (Without Replacement)
*
Step 1: Count the total number of candies.
$$ 4 + 6 + 3 + 5 + 2 = 20 \text{ candies} $$
*
Step 2: Find the probability of picking Blue first. There are 5 Blue candies out of 20.
$$ P(\text{Blue}) = \frac{5}{20} = \frac{1}{4} $$
*
Step 3: Find the probability of picking Yellow second. Since you ate the first candy, there are now only 19 left in the bowl. There are still 4 Yellow candies.
$$ P(\text{Yellow}) = \frac{4}{19} $$
*
Step 4: Multiply the probabilities.
$$ \frac{1}{4} \times \frac{4}{19} = \frac{4}{76} $$
This simplifies to $\frac{1}{19}$.
5. Pens (With Replacement)
*
Step 1: Count the total pens.
$$ 3 \text{ red} + 2 \text{ green} + 1 \text{ blue} = 6 \text{ pens} $$
*
Step 2: Find the probability of picking Red.
$$ P(\text{Red}) = \frac{3}{6} = \frac{1}{2} $$
*
Step 3: Find the probability of picking Green. Because you put the first pen back (
replacement), the total is still 6.
$$ P(\text{Green}) = \frac{2}{6} = \frac{1}{3} $$
*
Step 4: Multiply the probabilities.
$$ \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} $$
──────────────────────────────────────
Final Answer:
1. B
2. B
3. C
4. D
5. C
Parent Tip: Review the logic above to help your child master the concept of probability of compound events worksheet.
