Probability

 

PROBABILITY : DICE BASED QUESTIONS

Q1. An unbiased die is thrown. What is the probability of getting

1. an even number
2. a multiple of 3
3. a multiple of 2 or 3
4. a number less than 5 divisible by 2.
   
5. A number greater than 2 divisible by 3.
6. an even number or a multiple of 3
7. an even number and a multiple of 3
8. a number 3 or 4
9. an odd number
10. a number less than 5
11. a number greater than 3
12. a number between 3 and 6.

Q2. Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is (i) 6 (ii) 12 (iii) 7

 Q3. Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than 9.

 Q4. Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.

 Q5. Two dice are thrown at the same time. Determine the probabiity that the difference of the numbers on the two dice is 2.

 Q7. Two dice are thrown at the same time. Find the probability of getting (i) same number on both dice. (ii) different numbers on both dice.

 Q8. Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is (i) 7? (ii) a prime number? (iii) 1?

 Q9. Two dice are thrown simultaneously. Find the probability of getting

1. an even number on first dice
2. an odd number on first dice
3. an even number as the sum
4. a multiple of 5 as the sum
5. a multiple of 7 as the sum
6. a multiple of 3 as the sum
7. a sum more than 7
8. a sum greater than 9
9. neither the sum 9 nor the sum 11 as the sum
10. a sum less than 6
11. a sum less than 7
12. a sum more than 7
13. a multiple of 3 on one dice
14. a multiple of 2 on one dice
15. a multiple of 5 on one dice
16. a multiple of 2 on one dice and a multiple of 3 on the other
17. a doublet
18. a doublet of even number
19. a doublet of odd number
20. a doublet of prime number
21. a number other than 5 on any dice 
22. a number other than 3 on any dice               
23. the sum equal to 12.
24. the sum greater than equal to 10
25. the sum less than or equal to 10
26. the sum as a prime number

PROBABILITY : COINS BASED QUESTIONS

Q1. Two coins are tossed simultaneously. Find the probability of getting

1. at least one head
2. at most one head
3. exactly two head
4. exactly one head
5. no head
6. no tail
7. at least one tail
8. at most one tail
9. exactly two tails
   
10. exactly one tail

Q2. A coin is tossed two times. Find the probability of getting at most one head 

Q3. A coin is tossed 3 times. List the possible outcomes. Find the probability of getting (i) all heads (ii)        at least 2 heads

Q4. Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

Q5. If I toss a coin 3 times and get head each time, should I expect a tail to have a higher chance in the 4th toss? Give reason in support of your answer.

Q6. Three coins are tossed simultaneously. What is the probability of getting

1. exactly two heads
2. at least two heads
3. at most two heads
4. one head or two heads
5. exactly one tail
6. at least one tail
7. at most one tail
8. at least two tails
9. at most two tails
10. exactly two tails
11. no head
12. no tail

PROBABILITY : BAG BALLS BASED QUESTIONS

Q1. 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

red ?

not red?

(PLAYING CARDS BASED QUESTIONS) 

 1. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting 

 (a) an ace card 

 (b) a red card 

 (c) either red or king card 

 (d) red and a king 

 (e) ‘2’ of spades 

 (f) ‘10’ of a black suit 

 (g) a queen of black suit 

 (h) either a black card or a king 

 (i) black and king card 

 (j) a jack, queen or a king 

 (k) a heart card 

 (l) a queen card 

 (m) the ace of spades 

 (n) the seven of clubs 

 (o) a ten 

 (p) a black card 

 (q) neither a heart nor a king 

 (r) neither an ace nor a king 

 (s) neither a red card nor a queen card 

 (t) a face card or an ace 

 (u) a face card or a black card 

 (v) a face card and a black card 

 (w) neither a face card nor an ace 

 (x) neither a face card nor ’10’ card 

 (y) either a king or red card 

 (z) either an ace or black card 

 (aa) an ace and a black card