LEVEL-1
1. The probability that it will rain tomorrow is 0.85. What is the probability that it will no
rain tomorrow?
2. A die is thrown. Find the probability of getting:
(i) a prime number [NCERT, CBSE 2019] (ii) 2 or 4
(iii) a multiple of 2 or 3
(iv) an even prime number [CBSE 2008
(v) a number greater than 5[CBSE 2008] (vi) a number lying between 2 and 6
(vii) a composite number [CBSE 2019]
[NCERT, CBSE 2019
3. Three coins are tossed together. Find the probability of getting:
(i) exactly two heads
(ii) at most two heads
(ii) at least one head and one tail. (iv) no tails
4. A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher numbe
5. Two unbiased dice are thrown. Find the probability that the total of the numbers on th
dice is greater than 10.
[CBSE 2018
6. A card is drawn at random from a pack of 52 cards. Find the probability that the car
drawn is
(i) a black king
(ii) either a black card or a king
Answers
Solution 1 :-
The probability that it will be rain tomorrow is 0.85 .
As we know that,
P( E ) + P( not E ) = 1
Here, P ( E ) = 0.85
So,
1 - 0.85 = 0.15
Hence, The probability that it will be no rain tomorrow is 0.15
Solution 2 :-
( 1 )Total outcomes of die = 1 , 2 , 3 , 4 , 5 , 6 = 6
Favourable outcomes = 2 , 3 , 5 = 3
Therefore,
Probability = Favourable outcomes/Total outcomes
P( getting prime numbers ) = 3/6 = 1/2
( 2 ) Total outcomes of die = 6
Favourable outcomes = 2 or 4 = 1
P( getting 2 ) = 1/6
P( getting 4) = 1/6
(3) Multiple of 2 = 4 , 6 or 3 = 6
Total outcomes = 6
Favourable outcome = 2 or 1
Now,
P( getting multiple of 2) = 2/6 = 1/3
P( getting multiple of 3) = 1/6
4) Total outcomes = 6
Favourable outcomes = 2 , 4 , 6
P( getting even numbers) = 3/6 = 1/2
5) Total outcomes = 6
Favourable outcome = 1 ( only 6 is greater than 5)
P ( getting greater than 5) = 1 / 6
6) Total outcomes = 6
Favourable outcome = 3,4,5 = 3
P( getting numbers between 2 and 6 ) = 3/6 = 1/2
7) Total outcomes = 6
Favourable outcomes = 4 , 6
P( getting composite number) = 2/6 = 1/3
Solution 3 :-
Three coins are tossed together,
Total outcomes = 8 [ HHH, HTH, HHT, THH, HHT, THT, TTH , TTT ]
1) Exactly two heads
Total outcomes = 8
Favourable outcome = 3
P ( getting exactly 2 head) = 3/8
2) At most two heads
Total outcomes = 8
Favourable outcome = 4
P( getting At most 2 heads) = 4/8 = 1/2
3) Total outcomes = 8
Favourable outcome = 6
P( getting one head and one tail) = 6/8
4) Total Outcomes = 8
Favourable outcome = 1
P( getting no tails) = 1/8
Solution 4 :-
Total outcomes = 36
Favourable outcomes, = 9
Therefore,
P( chance of throwing B) = 9/36 = 1/4
Solution 5 :-
Total outcomes = 36
Favourable outcome = 3 ( (5,6), ( 6 ,5) , ( 6 ,6 ) )
P( getting greater than 10) = 3/36 = 12
Solution 6 :-
1) Total outcomes = 52
Total black king = 2
Favourable outcome = 2
P ( getting black king) = 2/52 = 1/26
2) Total outcomes = 52
Total black cards or black king = 28
Favourable outcome = 28
P( getting either black card or king)
= 28/52 = 7/13
Step-by-step explanation:
1..... 0.15
2.... {I} 1/2