Engineering Entrance Sample Papers

Probability Questions and Answers

probability questions

Probability Problems and Answers

Question 1
The probability of getting at least one tail in 4 throws of a coin is
A
None of these
B
1/16
C
15/16
D
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
A
None of these
B
1/4
C
1/3
D
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
A
6/5
B
18/5
C
1/5
D
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
A
None of these
B
1/7
C
13/15
D
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
A
3/16
B
1/4
C
1/32
D
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, is
A
1/2
B
7/15
C
3/5
D
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
A
At least 30
B
Exactly 25
C
At most 20
D
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
A
1/18
B
None of these
C
2/7
D
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

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A
49/101
B
1/2
C
51/101
D
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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A
5/9
B
4/9
C
1/2
D
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
A
3/5
B
3/4
C
4/5
D
2/3
Question 12
Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is
A
7/18
B
5/18
C
5/36
D
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
A
1/2
B
1/3
C
3/4
D
None of these
Question 14
The probability of getting a number greater than 2 in throwing a die is

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A
1/6
B
2/3
C
1/2
D
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
A
¾
B
7/18
C
5/12
D
½
Question 16
For an event, odds against is 6 : 5. The probability that event does not occur, is
A
1/6
B
5/6
C
6/11
D
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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A
2/5
B
4/5
C
1/5
D
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
A
2/5
B
1/2
C
2/3
D
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
A
None of these
B
10/133
C
9/133
D
9/1330
Question 20
If A and B are mutually exclusive events, then the value of P (A or B) is
A
None of these
B
0
C
–1
D
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
A
1/4
B
3/8
C
3/16
D
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
A
1/13
B
1/26
C
7/13
D
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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A
½
B
1/6
C
1/12
D
None of these
Question 24
Two dice are thrown simultaneously. The probability that sum is odd or less than 7 or both, is
A
2/3
B
3/4
C
1/3
D
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 to

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A
14
B
7
C
10
D
None of these
Question 26
Three coins are tossed together, then the probability of getting at least one head is
A
1/8
B
3/4
C
1/2
D
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

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A
< ½
B
½
C
> ½
D
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
A
1/2
B
2/3
C
1/3
D
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
A
1/2
B
20/39
C
14/29
D
None of these
There are 29 questions to complete.
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