Access Answers for SAT Maths Chapter 15 – Probability
Exercise: 15.1
1. Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ = ___________.
(ii) The probability of an event that cannot happen is __________. Such an event is called ________.
(iii) The probability of an event that is certain to happen is _________. Such an event is called
_________.
(iv) The sum of the probabilities of all the elementary events of an experiment is __________.
(v) The probability of an event is greater than or equal to ___ and less than or equal to __________.
Solution:
(i) Probability of an event E + Probability of the event ‘not E’ = 1.
(ii) The probability of an event that cannot happen is 0. Such an event is called an impossible event.
(iii) The probability of an event that is certain to happen is 1. Such an event is called a sure or certain
event.
(iv) The sum of the probabilities of all the elementary events of an experiment is 1.
(v) The probability of an event is greater than or equal to 0 and less than or equal to 1.
2. Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
(iii) A trial is made to Solution: a true-false question. The Solution: is right or wrong.
(iv) A baby is born. It is a boy or a girl.
Solution:
(i) This statement does not have equally likely outcomes as the car may or may not start depending
upon various factors like fuel, etc.
(ii) Even this statement does not have equally likely outcomes as the player may shoot or miss the
shot.
(iii) This statement has equally likely outcomes as it is known that the solution is either right or
wrong.
(iv) This statement also has equally likely outcomes as it is known that the newly born baby can
either be a boy or a girl.
3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at
the beginning of a football game?
Solution:
Tossing of a coin is a fair way of deciding because the number of possible outcomes are only 2 i.e.
either head or tail. Since these two outcomes are an equally likely outcome, tossing is unpredictable
and is considered to be completely unbiased.
, 4. Which of the following cannot be the probability of an event?
(A) 2/3 (B) -1.5 (C) 15% (D) 0.7
Solution:
The probability of any event (E) always lies between 0 and 1 i.e. 0 ≤ P(E) ≤ 1. So, from the above
options, option (B) -1.5 cannot be the probability of an event.
5. If P(E) = 0.05, what is the probability of ‘not E’?
Solution:
We know that,
P(E)+P(not E) = 1
It is given that, P(E) = 0.05
So, P(not E) = 1-P(E)
Or, P(not E) = 1-0.05
∴ P(not E) = 0.95
6. A bag contains lemon flavored candies only. Malini takes out one candy without looking into the
bag. What is the probability that she takes out
(i) an orange flavored candy?
(ii) a lemon flavored candy?
Solution:
(i) We know that the bag only contains lemon-flavored candies.
So, The no. of orange flavored candies = 0
∴ The probability of taking out orange flavored candies = 0/1 = 0
(ii) As there are only lemon flavored candies, P(lemon flavored candies) = 1 (or 100%)
7. It is given that in a group of 3 students, the probability of 2 students not having the same
birthday is 0.992. What is the probability that the 2 students have the same birthday?
Solution:
Let the event wherein 2 students having the same birthday be E
Given, P(E) = 0.992
We know,
P(E)+P(not E) = 1
Or, P(not E) = 1–0.992 = 0.008
∴ The probability that the 2 students have the same birthday is 0.008
8. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the
probability that the ball drawn is
Exercise: 15.1
1. Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ = ___________.
(ii) The probability of an event that cannot happen is __________. Such an event is called ________.
(iii) The probability of an event that is certain to happen is _________. Such an event is called
_________.
(iv) The sum of the probabilities of all the elementary events of an experiment is __________.
(v) The probability of an event is greater than or equal to ___ and less than or equal to __________.
Solution:
(i) Probability of an event E + Probability of the event ‘not E’ = 1.
(ii) The probability of an event that cannot happen is 0. Such an event is called an impossible event.
(iii) The probability of an event that is certain to happen is 1. Such an event is called a sure or certain
event.
(iv) The sum of the probabilities of all the elementary events of an experiment is 1.
(v) The probability of an event is greater than or equal to 0 and less than or equal to 1.
2. Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
(iii) A trial is made to Solution: a true-false question. The Solution: is right or wrong.
(iv) A baby is born. It is a boy or a girl.
Solution:
(i) This statement does not have equally likely outcomes as the car may or may not start depending
upon various factors like fuel, etc.
(ii) Even this statement does not have equally likely outcomes as the player may shoot or miss the
shot.
(iii) This statement has equally likely outcomes as it is known that the solution is either right or
wrong.
(iv) This statement also has equally likely outcomes as it is known that the newly born baby can
either be a boy or a girl.
3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at
the beginning of a football game?
Solution:
Tossing of a coin is a fair way of deciding because the number of possible outcomes are only 2 i.e.
either head or tail. Since these two outcomes are an equally likely outcome, tossing is unpredictable
and is considered to be completely unbiased.
, 4. Which of the following cannot be the probability of an event?
(A) 2/3 (B) -1.5 (C) 15% (D) 0.7
Solution:
The probability of any event (E) always lies between 0 and 1 i.e. 0 ≤ P(E) ≤ 1. So, from the above
options, option (B) -1.5 cannot be the probability of an event.
5. If P(E) = 0.05, what is the probability of ‘not E’?
Solution:
We know that,
P(E)+P(not E) = 1
It is given that, P(E) = 0.05
So, P(not E) = 1-P(E)
Or, P(not E) = 1-0.05
∴ P(not E) = 0.95
6. A bag contains lemon flavored candies only. Malini takes out one candy without looking into the
bag. What is the probability that she takes out
(i) an orange flavored candy?
(ii) a lemon flavored candy?
Solution:
(i) We know that the bag only contains lemon-flavored candies.
So, The no. of orange flavored candies = 0
∴ The probability of taking out orange flavored candies = 0/1 = 0
(ii) As there are only lemon flavored candies, P(lemon flavored candies) = 1 (or 100%)
7. It is given that in a group of 3 students, the probability of 2 students not having the same
birthday is 0.992. What is the probability that the 2 students have the same birthday?
Solution:
Let the event wherein 2 students having the same birthday be E
Given, P(E) = 0.992
We know,
P(E)+P(not E) = 1
Or, P(not E) = 1–0.992 = 0.008
∴ The probability that the 2 students have the same birthday is 0.008
8. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the
probability that the ball drawn is
