Class 10 Maths Chapter 20
Probability
Important Questions

In this chapter, we delve into class 10 probability important questions and answers through a collection of carefully chosen questions that will sharpen your skills, challenge your thinking, and deepen your grasp of this essential mathematical concept. Get ready to tackle a variety of probability scenarios as we work through these important questions, honing your ability to assess chances, make predictions, and solve real-life problems. Probability is not just about numbers; it's a tool that empowers us to make sense of randomness. These questions will guide you on a journey of discovery, helping you master the art of probability. As you embark on this chapter, you'll find a diverse range of questions that will not only prepare you for exams but also equip you with valuable problem-solving skills applicable in everyday life.

Introduction

The chapter on "Probability" is a captivating exploration of uncertainty and chance. Probability is the branch of mathematics that allows us to quantify and analyze the likelihood of events occurring. This chapter equips students with the tools to make informed predictions and decisions in real-world situations. Here's an introduction to the probability class 10 ICSE questions. Imagine you're making decisions in a world filled with uncertainties - from predicting the outcome of a cricket match to estimating the chances of rain on your picnic day. How do you navigate through these uncertainties? That's where the chapter on probability comes into play.

Key Concepts and Objectives:

Understanding Uncertainty: Probability begins by acknowledging that life is uncertain. You'll explore how to tackle situations where you can't predict the outcome with certainty.

Calculating Probabilities: You'll learn to calculate probabilities using mathematical techniques. Whether it's flipping a coin or drawing cards from a deck, you'll be equipped to find the chances of various outcomes.

Events and Outcomes: You'll delve into the concepts of events and outcomes. Events are the situations you're interested in (like winning a game), and outcomes are the possible results (like rolling a 6 on a dice).

What is Probability?

Ans: in Class 10 ICSE mathematics is the numerical measure of the likelihood of an event happening. It's expressed as a value between 0 (impossible event) and 1 (certain event). The higher the probability, the more likely the event is to occur.

In practical terms, probability allows us to analyze situations where there is uncertainty or randomness involved. It's widely used in various fields, including statistics, science, economics, and decision-making, to assess risks, make informed choices, and understand the chances of different outcomes.

Class 10 Probability Important Questions and Answers

Q1. The probability of passing students in a class is \(\frac{7}{38}\). What is the probability of failure in the class?

Options

(a) \(\frac{1}{38}\)
(b) \(\frac{31}{38}\)
(c)\(\frac{35}{38}\)
(d) \(\frac{7}{38}\)

Ans. (b) \(\frac{31}{38}\)

Explanation:
P(failure)=1-P (pass)                         [mutually exclusive]
=1-\(\frac{7}{38}\)=\(\frac{31}{38}\)

Q2. If a card is drawn from a well-shuffled deck of 52 cards, what is the probability of drawing a Jack?

Options

(a) 1/4
(b) 1/2
(c) 1/52
(d) 1/13

Ans. (d) 1/13
Explanation:
Total no. of possible outcomes n(S) = 52
        Number of favourable outcomes n(E) = 4
∴ Probability of drawing a jack = \(\frac{n(E)}{n(S)}\)=\(\frac{4}{52}\)=\(\frac{1}{13}\)

Q3. Three different coins are tossed together. Determine the probability of getting :
(i) exactly two heads.
(ii) atleast two heads.
(iii) atleast two tails.

Explanation:
Sample space for three coins tossed is 
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
⇒   n(S)=8
(i) Exactly two heads = {HHT, HTH, THH}
⇒ n(P1)=3
∴ P _1​ =\(\frac{n(p_1)}{n(S)}\)=\(\frac{3}{8}\).
(ii) Atleast two heads {HHT, HTH, THH, HHH}
⇒   n(P ₁)=3
∴ P ₂ =​ \(\frac{n(P_1)}{n(S)}\)=\(\frac{4}{8}\)=\(\frac{1}{2}\)
(iii) Atleast two tails {TTH, THT, HTT, TTT}  n(P₃)=4
P ₃​ = \(\frac{n(P_3)}{n(S)}\)=\(\frac{4}{8}\)=\(\frac{1}{2}\)

Q4. All the red face cards are removed from a pack of 52 playing cards. A card is drawn at random, determine the probability that a drawn card is :
(i) red colour
(ii) a queen
(iii) an ace
(iv) a face card

Explanation:
Since, the red face cards are removed, number of cards = 46.
∴  (i) P (of red colour)=\(\frac{20}{46}\)=\(\frac{10}{23}\)
(ii) P (a Queen)=\(\frac{2}{46}\)=\(\frac{1}{23}\)
(iii) P (an ace)=\(\frac{4}{46}\)=\(\frac{2}{23}\)
(iv) P (a face card)=\(\frac{6}{46}\)=\(\frac{3}{23}\)

Q5. Namita tossed a coin once. What is the probability of getting (i) Head, (ii) Tail ?

Explanation:
(i)Sample space,  
        S={H,T}
     n(S)=2  
    Event={Head}
‍n(E) =1
∴P(E) =\(\frac{n(E)}{n(S)}\)
⇒P(E) =\(\frac{1}{2}\)
(ii) Sample space S = {H, T}
⇒    n(S)=2 
   Event={Tail}
⇒n(E)=1
∴P(E)=\(\frac{n(E)}{n(S)}\)=\(\frac{1}{2}\)

ICSE Class 10 Maths Chapter wise Important Questions

Conclusion

In conclusion, the chapter on probability in Class 10 ICSE mathematics is a fascinating exploration of uncertainty and chance. It equips students with essential tools to understand and calculate probabilities, enabling them to make informed decisions and predictions in various real-life situations. Probability is not just a mathematical concept; it's a fundamental aspect of our daily lives, influencing everything from weather forecasts to game strategies.

By mastering the principles of probability, students gain a valuable skillset that extends beyond the classroom. They learn to assess risks, analyze data, and make rational choices in uncertain circumstances. Moreover, probability serves as a bridge to more advanced mathematical and scientific concepts, paving the way for future exploration and discovery.

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Frequently Asked Questions

Q1 : What is probability in mathematics?

Ans: Probability is a branch of mathematics that deals with the likelihood of events occurring. It quantifies uncertainty and helps us make predictions based on data.

Q2: How is probability expressed?

Ans:  Probability is often expressed as a value between 0 (impossible event) and 1 (certain event). The higher the probability, the more likely the event is to occur.

Q3 : What is an event in probability?

Ans: An event is a specific outcome or result of an experiment or situation. Events can be simple (single outcome) or compound (combination of outcomes).

Q4 : What is the difference between theoretical probability and experimental probability?

Ans: Theoretical probability is based on mathematical calculations, while experimental probability is determined through actual observations or experiments.

Q5 : How do you calculate the probability of an event?

Ans: Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. P(A) = Number of Favorable Outcomes / Total Possible Outcomes.