Chapter 15

Probability

The notes for CBSE chapter 15 class 10 maths are given in this section in detail. Let's take a look at the concept of probability, experimental probability, theoretical probability, and the many terminologies used in probability. Probability is a field of mathematics that evaluates the uncertainty about the occurrence of an event via the use of numbers. The probability that an event will take place or will not take place is stated on a scale ranging from 0 to 1.

Exercises of NCERT Solutions for Class 10 Maths Probability

  1. Which of the following experiments has the same chance of producing a positive result? Explain.

  2. A driver tries unsuccessfully to start his automobile but is unsuccessful. Starting the car is either a success or a failure.

  3. A basketball player tries to make a shot with the ball. She or he either makes or misses the shot.

  4. A true-false question is presented to the participants in a trial. The answer is either correct or incorrect.

  5. A child is born into the world. It's either a boy or a girl, depending on who you ask.

2. Fill in the blanks with the appropriate information:

  1. E is the product of the probability of an event E and the probability of an event 'not E.' = ___________.

  2. The likelihood of an event occurring that cannot occur is __________. This kind of incident is referred to as ________.

  3. The likelihood of an event occurring is the probability of it occurring. _________. This kind of incident is referred to as _________.

  4. The probability of all of the elementary occurrences in an experiment is equal to the sum of all of their probabilities. __________.

  5.  The likelihood of an event occurring is higher than or equal to ___ as well as being less than or equal to __________.

3. Why is it thought to be a fair method of determining which team should get the ball at the start of a football game when a coin toss is performed?

 

4. Which of the following cannot be true about the likelihood of an event occurring?

 

(A) 2/3 (B) -1.5 (C) 15% (D) 0.7

 

5. What is the chance of 'not E' occurring if P(E) = 0.05?

6. Only lemon-flavoured sweets are included inside a bag. Malini grabs one candy out of the bag without peeking inside it first. What is the likelihood that she will be successful?

 

(i) Is there a candy with orange flavouring?

(ii) Is there a lemon-flavoured candy?

 

7. For example, it is said that in a group of three students, the likelihood of two students sharing the exact birthdate is 0.992. In what percentage of cases do the two pupils have the same birthday?

 

8. Three red balls and five black balls are contained inside a bag. A ball is picked at random from the bag to represent each player. What is the likelihood that the ball drawn is the correct one?

(I) Red?

(II) Not red?

 

9. Five red marbles, eight white marbles, and four green marbles are contained inside a box. Every time a marble is plucked out of the box at random, the game is over. What is the likelihood that the stone that was taken out will be returned?

(i) red?

(ii) white?

(iii) not green?

 

10. A piggy bank includes hundred 50p coins, fifty ₹ one coins, twenty ₹ two coins, and ten ₹ five coins. The likelihood that one of the coins will fall out when the bank is flipped upside down is equal to one. What is the probability that the coin will not fall out?

 

(i) will it be a 50 p coin?

(ii) will it not be a ₹5 coin?

Answer 1)

  1. It is not an equally probable consequence since the automobile will not start if it is out of commission only when it is out of commission.

  2. It is not an equally probable conclusion since the outcome of this game is dependent on a variety of factors.

  3. Because both outcomes have an equal probability of occurring, they are both equally probable.

  4. Because both outcomes have an equal probability of occurring, they are both equally probable.

 

Answer 2)

(i) The probability of an event E plus the probability of an occurrence 'not E' equals one.

(ii) The likelihood of an event occurring that cannot occur is zero. An occurrence of this kind is referred to as an impossible event.

(iii) The likelihood of an event occurring is one if it is guaranteed to occur. A sure or definite occurrence is a situation in which a given outcome is inevitable.

(iv) 1 is the probability that all of the primary events in an experiment will occur at a specific rate.

(v) It is more likely than not that an event will occur when the probability of it occurring is higher than or equal to 0.

 

Answer 3).

The tossing of a coin is a reasonable method of deciding the number of potential outcomes is limited to two, i.e., either head or tail. Throwing a coin is unexpected since both results are equally possible; hence, it is believed to be entirely neutral.

 

Answer 4).

Whenever an event (E) occurs, the probability of it occurring is always between 0 and 1, which is expressed as 0 P(E) 1. As a result, option (B) -1.5 cannot represent the likelihood of an occurrence based on the possibilities listed above.

 

Answer 5).

We are well aware of this.

P(E) plus P(not E) equals one.

It is shown that P(E) = 0.05.

As a result, P(not E) = 1-P. (E)

Alternatively, P(not E) = 1-0.05

P(not E) = 0.95 in this case.

 

Answer 6).

(i) We are aware that the bag includes chocolates solely with lemon flavouring.

As a result, the number of orange-flavoured sweets is zero.

∴ Orange-flavoured sweets are less likely to be taken out than other candies.

(ii) P(lemon-flavoured candies) = one since there are only lemon flavoured sweets available (or 100 per cent)

 

Answer 7).

Let E represent the situation in which two students have the exact birthdate.

Assume that P(E) = 0.992.

We already know that P(E)+P(not E) = 1.

Alternatively, P(not E) = 1–0.992 = 0.008

The likelihood that the two pupils have the exact birthdate is 0.008 per cent.

 

Answer 8)

The total number of balls is the sum of the number of red balls and the number of black balls.

As a result, the total number of balls is 5+3 = 8.  We already know that the probability of an occurrence is defined as the ratio between the number of favourable outcomes and the total number of possible outcomes (or outcomes).

N = (number of favourable results / total number of outcomes) where N = number of positive outcomes

(i) The probability of drawing red balls is calculated as P (red balls) = (the number of red balls divided by the total number of balls) = 3/8.

(ii) P (black balls) = (the number of black balls divided by the total number of balls) = 5/8 is the probability of drawing black balls.

 

Answer 9)

The total number of balls is 5+8+4 = 17 balls.

N = (number of favourable results / total number of outcomes) where N = number of positive outcomes.

(i) The total number of red balls in the game is 5.

The red ball has a value of 5/17 = 0.29.

(ii) 8 white balls make up the total amount of white balls.

P (white ball) = 8/17 = 0.47 P (white ball)

(iii) The total number of green balls is equal to four.

(green ball) = 4/17 = 0.23 p (green ball) P (not green) = 1-P (green ball) = 1-(4/7) = 0.77. P (not green) = 1-P (green ball) = 1-(4/7) = 0.77.

Answer 10).

The total number of coins is 100 plus 50 plus 20 plus 10 equals 180.

N = (number of favourable results / total number of outcomes) where N = number of positive outcomes.

(i) The total number of 50-cent coins is 100.

A 50-peso coin is equal to 100/180 = 5/9 = 0.55.

(ii) The total number of 5 coins is equal to 10.

P (5 coin) = 10/180 = 1/18 = 0.055 P (5 coin) = 10/180 = 1/18 = 0.055

The product of P (not a 5-coin) and 1-P (a 5-coin) is 1-0.055 = 0.945

An event is a collection of outcomes that occur at the same time. As an example, when we roll a die, the likelihood of having a number fewer than five is considered an occurrence. Please keep in mind that an event may only have a single result. In this article, we studied the concept of probability, as well as experimental probability, theoretical probability, and the many terminologies used in probability. An outcome is a consequence of a random experiment that has occurred. For example, when we roll a die, the number six is one of the possible outcomes.

Refer to the Class 10 Probability Solutions mentioned above for more details.

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