Basic Probability Math Antics Video Exercises online exercise for ... - Free Printable

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

Problem 1: Flipping a Coin
* Goal: Find the probability of flipping "heads".
* Logic: A standard coin has two sides: heads and tails. There is only 1 "heads" side.
* Fraction: 1 out of 2, which is $\frac{1}{2}$.
* Decimal: $\frac{1}{2}$ equals $0.5$.
* Percentage: $0.5$ equals $50\%$.

Problem 2: Rolling a Die
* Goal: Find the probability of rolling a 2.
* Logic: A standard die has 6 sides (1, 2, 3, 4, 5, 6). There is only one side with a 2.
* Fraction: 1 out of 6, which is $\frac{1}{6}$.
* Likely or Unlikely? Since $\frac{1}{6}$ is a very small chance (less than half), it is considered unlikely.

Problem 3: Spinning a 5
* Goal: Find the probability of spinning a 5 on a 10-sector spinner.
* Logic: There are 10 total sectors. Assuming the numbers are 1 through 10, there is only one "5".
* Fraction: $\frac{1}{10}$.
* Decimal: $\frac{1}{10}$ equals $0.1$.
* Percentage: $0.1$ equals $10\%$.
* Probability Line: The line goes from 0 to 1, with $\frac{1}{2}$ in the middle. $\frac{1}{10}$ is very close to 0. You would place a dot on the first tick mark to the right of 0.

Problem 4: Choosing a Red Marble
* Goal: Find the probability of choosing a red marble.
* Logic: There are 3 red marbles and 1 blue marble.
* Total marbles = $3 + 1 = 4$.
* Red marbles = 3.
* Fraction: $\frac{3}{4}$.
* Decimal: $\frac{3}{4}$ equals $0.75$.
* Percentage: $0.75$ equals $75\%$.
* Probability Line: $\frac{3}{4}$ is the same as $0.75$, which is past the halfway point ($\frac{1}{2}$ or $0.5$) and closer to 1. You would place a dot on the third tick mark after $\frac{1}{2}$.

Problem 5: Spinner Questions
* Logic: Look at the spinner. It has 8 sections numbered 1 through 8.
* Grey sections: 2, 4, 6, 8 (4 sections).
* White sections: 1, 3, 5, 7 (4 sections).
* Total sections: 8.

* a. Probability of spinning an 8: There is one '8'. Probability = $\frac{1}{8}$.
* b. Probability of spinning a 4: There is one '4'. Probability = $\frac{1}{8}$.
* c. Probability of spinning a grey sector: There are 4 grey sectors. Probability = $\frac{4}{8}$. (This can be simplified to $\frac{1}{2}$).
* d. Probability of spinning a white sector: There are 4 white sectors. Probability = $\frac{4}{8}$. (This can be simplified to $\frac{1}{2}$).

Problem 6: Marble Bag Questions
* Logic: Look at the bag. There are 12 marbles total.
* Black marbles: 3
* Grey marbles: 3
* White marbles: 6
* Total: 12

* a. Probability of black: 3 black marbles out of 12. Fraction = $\frac{3}{12}$. (Simplifies to $\frac{1}{4}$).
* b. Probability of grey: 3 grey marbles out of 12. Fraction = $\frac{3}{12}$. (Simplifies to $\frac{1}{4}$).
* c. Probability of white: 6 white marbles out of 12. Fraction = $\frac{6}{12}$. (Simplifies to $\frac{1}{2}$).
* d. Probability of white OR grey: Count white (6) and grey (3) together. $6 + 3 = 9$. Fraction = $\frac{9}{12}$. (Simplifies to $\frac{3}{4}$).

Final Answer:
1. Fraction: 1/2, Decimal: 0.5, Percentage: 50%
2. Fraction: 1/6, Unlikely
3. Fraction: 1/10, Decimal: 0.1, Percentage: 10%, Dot placed at the first mark after 0
4. Fraction: 3/4, Decimal: 0.75, Percentage: 75%, Dot placed at the third mark after 1/2
5. a. 1/8, b. 1/8, c. 4/8 (or 1/2), d. 4/8 (or 1/2)
6. a. 3/12 (or 1/4), b. 3/12 (or 1/4), c. 6/12 (or 1/2), d. 9/12 (or 3/4)