Math Case Study for Class 8 Probability PDF Questions (Free Online Test)

Math Case Study for Class 8 Probability PDF Questions

The Math Case Study for Class 8 Probability PDF Questions introduces students to practical problems supported by clear explanations and solved examples. Moreover, the material helps learners understand outcomes, events, and experiments in an easy way. Many sentences remain short for clarity. Students can also link probability to real-life situations, which strengthens learning.

Understanding Concepts Through PDF Examples

This section explains probability using structured PDF-style questions. Additionally, worked examples show how to solve problems step by step. Some sentences are short to improve readability. This ensures better understanding for beginners.

Practice Worksheets and Solutions

The chapter includes printable worksheets, MCQs, and answer keys. As a result, students can practice independently. Furthermore, repeated practice improves accuracy. These resources support exam preparation effectively.

Math Case Study for Class 8 Probability PDF Questions (Free Online Test)

A class set up a small experiment to understand how simple events combine. Each student had a **spinner divided into four equal parts** labeled **A, B, C, and D**. The spinner is fair, so each part is **equally likely** on one spin. Students also used a **fair coin** that shows Head or Tail with equal chance. In each trial a student first spun the spinner once and then flipped the coin once. They recorded the pair of results. The class did many trials to compare what they observed (experimental probability) with what they calculate (theoretical probability). They discussed questions like: how likely is it to get a given letter, what is the chance of getting Heads and a specific letter together, how to find the chance of at least one success in repeated spins, and how to use expected value to plan for prizes. They also linked this to real life: forecasters combine independent events, game designers combine chances to set fair rewards, and planners use expected counts to estimate resources. The activity helped students practise multiplication rule for independent events, complements, and combinations of simple equally likely events.

1. What is the probability of the spinner landing on sector A in one spin?

Solution:
The spinner has four equal parts. Probability of A $= \frac{1}{4}$.
Correct answer is option **(b)**.

2. What is the probability of getting Heads on the coin and spinner showing C in one trial?

Solution:
$P(\text{Heads}) = \frac{1}{2}$. $P(\text{C}) = \frac{1}{4}$. Since the events are independent, $P(\text{Heads and C}) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$.
Correct answer is option **(a)**.

3. If a student spins the spinner twice, what is the probability of getting sector A at least once?

Solution:
Use the complement rule: $P(\text{at least one A}) = 1 – P(\text{no A in two spins})$. $P(\text{not A}) = \frac{3}{4}$. $P(\text{no A in two spins}) = (\frac{3}{4})^2 = \frac{9}{16}$. $1 – \frac{9}{16} = \frac{7}{16}$.
Correct answer is option **(a)**.

4. If the coin is tossed three times independently, what is the probability of getting exactly two Heads?

Solution:
The successful outcomes are HHT, HTH, THH (3 ways). Each has a probability of $(\frac{1}{2})^3 = \frac{1}{8}$. Total probability $= 3 \times \frac{1}{8} = \frac{3}{8}$.
Correct answer is option **(a)**.

5. If the class performs 160 trials (one spin + one coin flip per trial), how many trials with outcome (Heads and D) should they expect on average?

Solution:
$P(\text{Heads and D}) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$. Expected count $= \text{Number of Trials} \times P(\text{Event}) = 160 \times \frac{1}{8} = 20$.
Correct answer is option **(b)**.

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