CBSE Class 10-Mathematics: Chapter – 15 Probability Part 14 (For CBSE, ICSE, IAS, NET, NRA 2023)
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Question 2:
A dice is thrown once. Find the probability of getting:
(i) A prime number.
(ii) A number lying between 2 and 6.
(iii) An odd number.
Answer:
Total number of favourable outcomes of throwing a dice
(i) On a dice, the prime numbers are and 5.
Therefore, favourable outcomes
Hence P (getting a prime number)
(ii) On a dice, the number lying between and 6 are .
Therefore, favourable outcomes
Hence
(iii) On a dice, the odd numbers are and .
Therefore, favourable outcomes
Hence P (getting an odd number)
Question 3:
A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e.. , three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.
Answer:
The outcomes associated with the experiment in which a coin is tossed thrice:
HHH, HHT, HTH, THH, TTH, HTT, THT, TTT
Therefore, Total number of favourable outcomes
Number of favourable outcomes
Hence required probability
Question 4:
A die is numbered in such a way that its faces show the numbers . It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:
Answer:
Complete table is as under:
It is clear that total number of favourable outcomes
(i) Number of favourable outcomes of getting total score even are
Hence P (getting total score even)
(ii) Number of favourable outcomes of getting total score 6 are 4
Hence P (getting total score 6)
(iii) Number of favourable outcomes of getting total score at least 6 are 15
Hence P (getting total score at least 6)
Question 5:
18 cards numbered 1,2, 3, … 18 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probabilities that the card bears
(i) an even number
(ii) a number divisible by 2 or 3
Answer:
Total no. of possible outcomes = 18
(i) Favorable cases are 2, 4, 6, 8, 10, 12,14, 16,18 i.e.. , 9 in number
Required probability
(ii) Favorable cares are i.e.. , in number
Required probability