Probability and Algebra
Practice questions covering probability theory and algebraic equations
Questions
Two cards are drawn, at random, from a pack of 52 cards. What is the probability of getting at least a spade and an ace?
- 1/34
- 8/221
- 2/51
- 1/26
- -
Four persons are to be chosen, at random, from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them will be children is
- 10/21
- 1/6
- 1/3
- 5/11
- -
A man and a woman appear for two vacancies for the same post. The probability of the man's selection is 1/4 and that of the woman's is 1/3. The probability that none of them will get selected is
- 1/2
- 1/3
- 1/4
- 1/5
- -
From a pack of 52 cards, one card is drawn at random. The probability that it is either a king or a queen is
- 1/13
- 2/13
- 3/20
- 2/5
- -
Three dice are rolled. What is the probability that the sum of the numbers, shown on the dice, is neither 3 nor 18?
- 1/36
- 5/36
- 1/108
- 107/108
- -
A and B went to a hotel. A paid Rs. 84 for 3 plates of idli and 5 plates of dosa. Whereas B took 5 plates of idli and 3 plates of dosa and paid Rs. 76. What is the cost of one plate of Idli?
- Rs. 6
- Rs. 8
- Rs. 10
- Rs. 12
- Rs. 15
Solve for x:
3x + 4/x - 3 = 2/3
- x = – 2
- x = – 18/7
- x = 18/7
- x = 2
- None of these
One ticket is drawn at random from a bag containing 30 tickets numbered from 1 to 30. What is the probability that it is a multiple of 3 or 5?
- 7/15
- 2/5
- 1/2
- 1/5
- -
The odds in favour of winning a game of chess, against b, are 5/2. If three games are to be played, the odds in favour of a's winning, at least in one game, are
- 335/8
- 1/2
- 8/335
- None of these
- -
The odd against a certain event is 5/2 and the odds in favour of another independent event is 6/5. The probability that none of the events will occur is
- 6/11
- 5/11
- 52/77
- 25/77
- -
A cricket club has 20 members. Out of them, only 8 can bowl. If 20 chits, bearing the names of each of them, are put in an urn and 11 are drawn at random. The chance of obtaining at least 5 bowlers, out of them, is
- 5/864
- 781/8398
- 3905/8398
- None of these
- -
Two persons a and b toss a coin, alternately, till one of them gets a heads and wins the game. What is their respective probabilities of winning?
- 2/3, 1/3
- 1/5, 2/7
- 1/3, 2/7
- 1/5, 1/3
- -
Find the values of x and y from the equations – = 1 and + = 3.5.
- x = 2, y = 3
- x = 4, y = 3
- x = 4, y = 9
- x = 2, y = 9
- None of these
Find x and y from 1/x - y + 5/3x - 2y = 2 and 15/3x - 2y = 2 - 2/x - y = 1.
- x = 3, y = 2
- x = 2, y = 3
- x = 4, y = 5
- x = 5, y = 4
- x = 1, y = 4
Aman won a competition and got some prize money. He gave Rs. 2,000 less than half of the money to his son and Rs. 1,000 more than two-thirds of the remaining to his daughter. If both get the same amount, what prize money did Aman get?
- Rs. 12,000
- Rs. 16,000
- Rs. 20,000
- Rs. 24,000
- Rs. 26,000