NCERT Solutions Class 7 Maths Chapter 3 Exercise 3.4: Data Handling

Understanding Chance and Probability

When we say 'it will probably rain today' or 'there is no chance of our team losing', we are talking about likelihood. In mathematics, we transition from these vague, everyday terms to a exact numerical value called Probability. An event is a outcome of an experiment that may or may not occur. In Exercise 3.4, you will classify statements into three categories:

1. Certain to happen: Events that are 100% guaranteed to take place (e.g., the Sun rising in the East).
2. Impossible: Events that can never happen under any circumstances (e.g., a tossed coin landing on both heads and tails simultaneously).
3. Can happen but not certain: Events that have a chance of occurring but are not guaranteed (e.g., getting a 6 when throwing a fair die). Developing this logical intuition is key to solving CBSE problems accurately.

Important Terminology

Random Experiment

An activity or test where the exact outcome cannot be predicted in advance, though all possible outcomes are known.

Outcome

The result of a single trial of an experiment. For example, getting a Head is an outcome of a coin toss.

Favorable Outcome

An outcome that satisfies the specific condition or event we are interested in.

Probability Formula

Probability of an Event, P(E) = (Number of Favorable Outcomes) / (Total Number of Equally Likely Outcomes).

How to Calculate Basic Probability

1. Step 1: Identify Total Outcomes — List every single possible result of the experiment. For example, if you roll a die, the total outcomes are {1, 2, 3, 4, 5, 6}. The total count is 6.
2. Step 2: Find Favorable Outcomes — Identify which of those outcomes fit your event criteria. If the event is 'getting an odd number', the favorable outcomes are {1, 3, 5}. The count of favorable outcomes is 3.
3. Step 3: Apply the Formula — Divide the number of favorable outcomes by the total number of outcomes. In our example: P(Odd Number) = 3 / 6 = 1/2 or 0.5.
4. Step 4: Express the Final Fraction — Always reduce the fraction to its simplest form. Write your final answer clearly with units if applicable (though probability is a unitless ratio).

Exam Tips & Common Mistakes to Avoid

1. Probability Values are Restricted: Remember that the probability of any event is always a number between 0 and 1 (inclusive). It can never be negative, and it can never be greater than 1! If you calculate a probability of 1.5 or -0.2, you have made a mathematical error.

2. Don't Confuse 'Impossible' with 'Unlikely': An event that has a very small chance of happening (like winning a lottery) is not 'impossible'; it belongs to the 'can happen but not certain' category. Only events that are physically or logically mathematically blocked can be labeled 'impossible'.

3. Equally Likely Outcomes: Ensure the outcomes of your experiment are fair. Standard CBSE questions assume coins are unbiased, dice are fair, and marbles are picked at random without looking.

Class 7 Data Handling Ex 3.4 Solved Problems

• Q: State whether the following is certain to happen, impossible, or can happen but not certain: 'You are older today than yesterday.' A: Step 1: Analyze the statement. Step 2: Time flows forward naturally, making everyone older with each passing day. This is a scientific fact. Step 3: Since it is guaranteed to happen, we classify it. Final answer: Certain to happen.
• Q: There are 6 marbles in a box with numbers from 1 to 6 marked on each of them. What is the probability of drawing a marble with number 2? A: Step 1: Identify total outcomes. The marbles are numbered {1, 2, 3, 4, 5, 6}. So, Total number of outcomes = 6. Step 2: Identify favorable outcomes. There is only one marble with the number 2. So, Number of favorable outcomes = 1. Step 3: Apply the formula. P(drawing 2) = (Favorable outcomes) / (Total outcomes). Final answer: 1/6
• Q: A coin is flipped to decide which team starts the game. What is the probability that your team will start? A: Step 1: Identify total outcomes. A flipped coin can land on either Head (H) or Tail (T). Total outcomes = 2. Step 2: Identify favorable outcomes. Your team chooses either Head or Tail. Only one of these will appear. Favorable outcomes = 1. Step 3: Apply the formula. P(starting) = 1/2. Final answer: 1/2 (or 50%)
• Q: A die is tossed once. What is the probability of getting a number greater than 4? A: Step 1: Find total outcomes of rolling a die. The possible outcomes are {1, 2, 3, 4, 5, 6}. Total outcomes = 6. Step 2: Find favorable outcomes. The numbers greater than 4 are {5, 6}. Number of favorable outcomes = 2. Step 3: Calculate the probability. P(greater than 4) = 2/6. Step 4: Simplify the fraction to its lowest terms. 2/6 = 1/3. Final answer: 1/3

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