Telangana SCERT Solution Class X (10) Maths Chapter 13 Probability Exercise 13.1
Exercise – 13.1
(1) Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ = 1
=> E and not E are the complementary events. So, sum of the probabilities of two complementary events = 1
(ii) The probability of an event that cannot happen is 0 such an event is called impossible even.
(iii) The probability of an event that is certain to happen is 1 such an event is called 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
=> Probability is always lies between 0 & 1
(Q2) 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.
=> Not equally likely outcomes.
(ii) A player attempts to shoot a basket ball she/he shoots or misses the shot.
=> Not equally likely outcomes.
(iii) A trial is made to answer a true – false question. The answer is right or wrong.
=> Equally likely outcomes.
(iv) A baby is born. It is a boy or a girl.
=> Equally likely outcomes.
(Q3) If P(E) = 0.05, what is the probability of ‘not E’?
=> Solution: We know,
P(E) + P(not E) = 1
= P(not E) = 1 – P(E)
= 1 – 0.05
P(not E) = 0.95
(Q4) 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) Since there are only lemon flavored candies in the bag it is impossible to come an orange flavored candy.
∴ P (an orange flavored candy) = 0
(ii) If she takes out a candy definitely it will be lemon flavored.
∴ P (a lemon flavored candy) = 1
(Q5) Rahim removes all the heats from the cards. What is the probability of –
(i) Getting an ace from the remaining pack.
(ii) Getting a diamonds.
(iii) Getting a card that is not a heart.
(iv) Getting the Ace of hearts
Deck of cards = 52
Hearts = 13
Remaining cards = 52-13
= 39
Total number of possible outcomes =
(i) Getting an ace
Favourable outcomes = 3
P(an ace) = 3/39
= 1/13
(ii) Getting a diamonds
Favourable outcomes = 13
P (a diamond) = 13/39
= 1/3
(iii) Not a heart
Favourable outcomes = 39
P (not a heart) = 39/39 = 1
(iv) Ace of heart
Favourable outcomes = 0
∴ P (ace of heart) = 0/39 = 0
(Q6)
(Q7) A dice is rolled once. Find the probability of getting
(i) A prime number
(ii) A number lying between 2 and 6
(iii) An odd number
=> Solution:
Here, total possible outcomes = 6 {1, 2, 3, 4, 5, 6)
(i) A prime number
Favourable outcomes = 3 {2, 3, 5}
P (a prime number) = 3/6 = 1/2
(ii) A number between 2 and 6
Favourable outcomes = 3 {3, 4, 5}
P (a number between 2 and 6) = 3/6 = 1/2
(iii) An odd number
Favourable outcomes = 3 {1, 3, 5}
P (an odd number) = 3/6 – 1/2
(Q8) What is the probability of selecting a red king from a deck of cards?
Solution:
Total number of cards = 52
Total possible outcomes = 52
‘a red king’ favourable outcomes = 2
P (a red king) = 2/52 = 1/26
(Q9) Make 5 more problems of this kind using dice. Cards or birthdays and discus with friends and teacher about their solutions.
(i) A dice is rolled once. Find the probability of getting a composite number?
(ii) A dice is rolled once. Find the probability of not getting an even number?
(iii) What is the probability of selecting a black card from a deck of cards?
(iv) What is the probability of selecting a face card from a deck of cards?
(v) Ravi and Raju are friends what is the probability that both will have the same birthday in a year (not leap year)?
=> Solution:
(i) Here, total number of possible outcomes = 6 {1,2, 3, 4, 5, 6}
Favourable outcomes = 2 = {4, 6}
P (getting a composite number) = 2/6
= 1/3
(ii) Total number of possible outcomes = 6 {1, 2, 3, 5, 6}
Favourable outcomes not an even number = {1, 3, 5} = 3
P (getting not an even number) = 3/2
= 1/2
(iii) Total number of cards = 52
Total possible outcome = 52
Black cards = 26 & Red cards = 26
Favourable outcomes = 26
P (Black cards) = 26/52
= 1/2
(iv) Deck of cards = 52
Total possible outcome = 52
Face cards = 12
Favourable outcomes = 12
P (face card) = 12/52
= 3/13
(5) Favourable outcomes = 1
P (Same year birthday) = 1/365
Here is your solution of Telangana SCERT Class 10 Math Chapter 13 Probability Exercise 13.1
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Explanation is verrgood I understand all the problems
Thank you scert team for your support