Quizzes / CBSE / Class 7 / Mathematics / Probability

Conducting Experiments Quiz - CBSE Class 7 Mathematics

Free practice quiz: Conducting Experiments (CBSE Class 7 Mathematics). 12 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 12 multiple-choice questions on Conducting Experiments, and 12 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Start quiz: 12 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

Probability of an Event

Probability measures how likely an event is, using outcomes that are all equally likely.
Count the favourable outcomes, then divide by the total number of possible outcomes.
Probability is always between 0 (impossible) and 1 (certain).

Basic probability

\[P(E)=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}\]

Range of probability

\[0 \le P(E) \le 1\]

Common mistake: Counting the total outcomes wrongly, for example forgetting some faces, sections or cards, so the denominator is wrong.

Complement: Event Not Happening

The event either happens or does not happen, so the two probabilities add to 1.
Use this when 'not' appears, or when counting the opposite case is easier.

Complement rule

\[P(\text{not } E)=1-P(E)\]

Common mistake: Forgetting to subtract from 1 and giving P(E) itself as the answer for 'not E'.

Either-Or Events: Add

If two events cannot happen at the same time, they are mutually exclusive.
For 'A or B' with such events, add their probabilities.
A standard deck has 52 cards, with 13 cards in each suit.

Mutually exclusive events

\[P(A \text{ or } B)=P(A)+P(B)\]

Common mistake: Adding probabilities when outcomes overlap, which counts some outcomes twice. Check that no outcome belongs to both events.

Independent Events: Multiply

Events are independent if one result does not change the other, like separate coin tosses or die rolls.
For 'A and B' with independent events, multiply their probabilities.

Independent events

\[P(A \text{ and } B)=P(A)\times P(B)\]

Same event n times

\[P(E \text{ every time})=\left(P(E)\right)^{n}\]

Common mistake: Adding the probabilities instead of multiplying when both events must happen together.

Drawing Without Replacement

If an item is not put back, the total decreases by one for the next draw.
The number of favourable items left may also decrease. Multiply the changed probabilities.

Two draws of a kind, no replacement

\[\frac{r}{n}\times\frac{r-1}{n-1}\]

Dependent events

\[P(A \text{ then } B)=P(A)\times P(B \text{ after } A)\]

Common mistake: Using the same fraction for every draw, as if items were replaced, when the question says items are drawn together or not returned.

Exam tips

List the sample space first so you know the total number of possible outcomes.
Keywords help: 'or' means add, 'and' means multiply, 'not' means subtract from 1.
Always simplify your final fraction and check that it lies between 0 and 1.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the probability of landing on heads when you flip a fair coin?
Show answer
Answer: A. 1/2
A fair coin has two sides: heads and tails. Since it is equally likely to land on either side, the probability is 1/2.
If you roll a six-sided die, what is the probability of rolling an even number?
Show answer
Answer: B. 1/2
The even numbers on a six-sided die are 2, 4, and 6, giving 3 successful outcomes. There are 6 possible outcomes, so the probability is 3/6, which simplifies to 1/2.
In a deck of cards, what is the probability of drawing a heart or a spade?
Show answer
Answer: A. 1/2
There are 13 hearts and 13 spades in a standard deck, totaling 26 cards. So the probability is 26/52, which simplifies to 1/2.
What is the probability of drawing a face card (Jack, Queen, King) from a deck of cards?
Show answer
Answer: A. 3/13
There are 12 face cards in a deck of 52 cards. Hence, the probability is 12/52, which simplifies to 3/13.
In a standard deck of cards, what is the probability of drawing two consecutive hearts?
Show answer
Answer: A. 1/17
The probability of drawing the first heart is 13/52. After drawing one heart, 12 hearts are left in a 51-card deck, giving a 12/51 chance. Thus, (13/52) * (12/51) = 1/17.