NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.4 | 2026-27

Think and Reflect

Question 1.

Can you calculate the probability of getting one head and one tail?

Solution:

Given: Two fair coins are tossed.

To find: The probability of getting one head and one tail.

The sample space for tossing two coins is:

S = {HH, HT, TH, TT}

where (H) represents Head and (T) represents Tail.

Thus, there are 4 possible outcomes.

The outcomes with one Head and one Tail are:
HT,\ TH

So, the number of favourable outcomes is 2.

Now, P(one head and one tad) = $\dfrac{\text{Favourable outcomes}}{\text{Total outcomes}}$

= $\dfrac{2}{4}$

= $\dfrac{1}{2}$

When two coins are tossed, getting one head and one tail can happen in two different ways (HT, TH), so the probability is $\dfrac{1}{2}$.

Exercise Set 7.4

Question 1.

There are two fruit baskets, A and B. Basket A has one apple and two oranges. Basket B has one banana and one mango. You randomly pick one fruit from each basket.

(i) Draw a tree diagram showing all possible pairs of fruits.

(ii) List the sample space.

(iii) What is the probability of picking one apple and one banana?

Solution:

(i) Tree Diagram showing all possible pairs of fruits

Each fruit from Basket A is paired with each fruit from Basket B.
Therefore, total outcomes = 3 × 2 = 6.

(ii) Sample Space (S) = {(A, B), (A, M), (O1, B), (O1, M), (O2, B), (O2, M)}
Number of all possible outcomes = 6

(iii) Probability of picking one apple and one banana
Number of favourable outcomes = 1 (only the pair (A, B))
Number of all possible outcomes = 6
P(Apple and Banana) = $\dfrac{\text{Number of Favourable outcomes}}{\text{Number of Total outcomes}}$

=  $\dfrac{1}{6}$

= 0.167 or 16.7%

Question 2.

Let us say that you have a box containing 3 red pens, 4 black pens, and 2 green pens. You pick a pen (without looking) from the box and put it back. Then your friend does the same.

(i) What are the possible outcomes of the pen colours? Can you draw a tree diagram representing the possible outcomes?

(ii) Can you use the tree diagram to guess the probability that both you and your friend pick pens of the same colour?

Solution:

(i) Since you put the pen back, the second person has the same choices as the first.

The possible colours are Red (R), Black (B), and Green (G).

The possible outcome pairs are:

(R, R), (R, B), (R, G), (B, R), (B, B), (B, G), (G, R), (G, B), (G, G)

Since the pen is replaced after the first pick, the number of possible outcomes remains the same for both selections.

Sample Space (S) = {(R, R), (R, B), (R, G), (B, R), (B, B), (B, G), (G, R), (G, B), (G, G)}

Number of all possible outcomes = 9

P(Red) = $\dfrac{3}{9}$

P(Black) = $\dfrac{3}{9}$

P(Green) = $\dfrac{3}{9}$

(ii) Yes. To find the probability that both of us pick the same colour, we consider the three matching outcomes: (R, R), (B, B), and (G, G).

We find the probability of each matching outcome and then add them together.

Both Red:

P(R, R) = 3/9 × 3/9 = 9/81

Both Black:

P(B, B) = 4/9 × 4/9 = 16/81

Both Green:

P(G, G) = 2/9 × 2/9 = 4/81

Total probability = 9/81 + 16/81 + 4/81 = 29/81

P(Same colour) = 29/81 = 0.358 or 35.8%

The tree diagram shows the three possible matching outcomes. The probability of each outcome depends on the number of pens of that colour in the box.

How Vedantu’s Class 9 Maths Exercise 7.4 Solutions Help You

Vedantu’s Class 9 Maths Exercise 7.4 Solutions are designed to make practice and revision easier. The step-by-step answers help students understand the method used to solve each question instead of relying only on the final answer.

• Understand the solving approach: Follow each step to see how the answer is derived and identify the concepts used.

• Practise independently: Try the questions yourself first and use the solutions to check your method and final answer.

• Clear doubts quickly: Simple explanations make it easier to identify and correct mistakes while practising Ex 7.4 Class 9.

• Revise before exams: Use the solutions to revisit key concepts and practise exercise questions efficiently.

• Learn at your own pace: Refer to the detailed NCERT Solutions for Class 9 Maths whenever you need additional support with a question.

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