## Probability Problems and Answers

Question 1 |

The probability of getting at least one tail in 4 throws of a coin is

None of these | |

1/16 | |

15/16 | |

1/4 |

Question 2 |

A box contains 10 red balls and 15 green balls. If two balls are drawn in succession then the probability that one is red and other is green, is

None of these | |

1/4 | |

1/3 | |

1/2 |

Question 3 |

A five digit number is formed by writing the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then the probability that the number is divisible by 4 is

6/5 | |

18/5 | |

1/5 | |

3/5 |

Question 4 |

A box contains 100 tickets numbered 1, 2 ...... 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number on them is 5 with probability

None of these | |

1/7 | |

13/15 | |

1/8 |

Question 5 |

If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is

3/16 | |

1/4 | |

1/32 | |

13/32 |

Question 6 |

A bag

*x*contains 3 white balls and 2 black balls and another bag*y*contains 2 white balls and 4 black balls. A bag and a ball out of it are picked at random. The probability that the ball is white, is1/2 | |

7/15 | |

3/5 | |

None of these |

Question 7 |

In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

At least 30 | |

Exactly 25 | |

At most 20 | |

None of these |

Question 8 |

Two squares are chosen at random on a chess-board. The probability that they have a side in common, is

1/18 | |

None of these | |

2/7 | |

1/9 |

Question 9 |

One hundred identical coins each with probability

*p*of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of*p*is**Related:** JEE Trigonometry Practice Questions

49/101 | |

1/2 | |

51/101 | |

50/101 |

Question 10 |

A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all, is

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5/9 | |

4/9 | |

1/2 | |

2/9 |

Question 11 |

A problem of mathematics is given to three students whose chances of solving the problem are 1/3, 1/4 and 1/5 respectively. The probability that the question will be solved is

3/5 | |

3/4 | |

4/5 | |

2/3 |

Question 12 |

Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is

7/18 | |

5/18 | |

5/36 | |

7/36 |

Question 13 |

A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is

1/2 | |

1/3 | |

3/4 | |

None of these |

Question 14 |

The probability of getting a number greater than 2 in throwing a die is

1/6 | |

2/3 | |

1/2 | |

1/3 |

Question 15 |

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

¾ | |

7/18 | |

5/12 | |

½ |

Question 16 |

For an event, odds against is 6 : 5. The probability that event does not occur, is

1/6 | |

5/6 | |

6/11 | |

5/11 |

Question 17 |

A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then the probability that 5 comes before 7 is

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2/5 | |

4/5 | |

1/5 | |

None of these |

Question 18 |

An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed is

2/5 | |

1/2 | |

2/3 | |

1/5 |

Question 19 |

Out of 21 tickets marked with numbers from 1 to 21, three are drawn at random. The chance that the numbers on them are in A.P., is

None of these | |

10/133 | |

9/133 | |

9/1330 |

Question 20 |

If

*A*and*B*are mutually exclusive events, then the value of*P*(*A*or*B*) isNone of these | |

0 | |

–1 | |

1 |

Question 21 |

A determinant is chosen at random. The set of all determinants of order 2 with elements 0 or 1 only. The probability that value of the determinant chosen is positive, is

1/4 | |

3/8 | |

3/16 | |

None of these |

Question 22 |

A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is

1/13 | |

1/26 | |

7/13 | |

1/2 |

Question 23 |

One die and one coin are tossed simultaneously. The probability of getting 6 on die and head on coin is

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½ | |

1/6 | |

1/12 | |

None of these |

Question 24 |

Two dice are thrown simultaneously. The probability that sum is odd or less than 7 or both, is

2/3 | |

3/4 | |

1/3 | |

1/2 |

Question 25 |

A fair coin is tossed

*n*times. Let*X*be the number of times head is observed. If P(X = 4), P(X = 5) and P(X = 6) are in H.P., then*n*is equal to14 | |

7 | |

10 | |

None of these |

Question 26 |

Three coins are tossed together, then the probability of getting at least one head is

1/8 | |

3/4 | |

1/2 | |

7/8 |

Question 27 |

Two persons ‘

*A*’ and ‘*B*’ have respectively n + 1 and*n*coins which they toss simultaneously. Then the probability that*A*will have more heads than*B*is**Related:** Halogen containing Compounds (Chemistry) Sample Paper

< ½ | |

½ | |

> ½ | |

None of these |

Question 28 |

*A*and

*B*toss a coin alternatively, the first to show a head being the winner. If

*A*starts the game, the chance of his winning is

1/2 | |

2/3 | |

1/3 | |

5/8 |

Question 29 |

Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

1/2 | |

20/39 | |

14/29 | |

None of these |

There are 29 questions to complete.

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