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Probability Quiz – 1

Question 1

Time: 00:00:00
A year is selected at random. What is the probability that it contains 53 Mondays if every fourth year is a leap year?

5/28

5/28

3/22

3/22

1/7

1/7

6/53

6/53

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Question 2

Time: 00:00:00
There are three cartons, each containing a different number of soda bottles. The first carton has 10 bottles, of which four are flat, the second has six bottles, of which one is flat, and the third carton has eight bottles of which three are flat. What is the probability of a flat bottle being selected when a bottle is chosen at random from one of the three cartons?

25/62

25/62

113/360

113/360

123/360

123/360

113/180

113/180

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Question 3

Time: 00:00:00
A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A∪B) is

2/5

2/5

3/5

3/5

1

1

1/4

1/4

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Question 4

Time: 00:00:00
One ticket is selected at random from 50 tickets numbered 0, 01, 02, ……, 49.Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero equals

1/14

1/14

1/7

1/7

5/14

5/14

1/50

1/50

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Question 5

Time: 00:00:00
In a plane, S lines of lengths 2, 3, 4, 5 and 6 cm are lying. What is the probability that by joining the three randomly chosen lines end to end a triangle cannot be formed?

\frac{3}{10}

\frac{3}{10}

\frac{7}{10}

\frac{7}{10}

\frac{1}{2}

\frac{1}{2}

1

1

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Question 6

Time: 00:00:00
There are 7 boys and 8 girls in a class. A teacher has 3 items viz a pen, a pencil and an eraser, each 5 in number. He distributes the items, one to each student. What is the probability that a boy selected at random has either a pencil or an eraser?

2/3

2/3

2/21

2/21

14/45

14/45

None of these

None of these

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Question 7

Time: 00:00:00
A locker at the RBI building can be opened by dialling a fixed three digit code (between 000 and 999). Chhota Chetan, a terrorist, only knows that the number is a three digit number and has only one six. Using this information he tries to open the locker by dialling three digits at random. The probability that he succeeds in his endeavor is

\frac{1}{243}

\frac{1}{243}

\frac{1}{900}

\frac{1}{900}

\frac{1}{1000}

\frac{1}{1000}

\frac{1}{216}

\frac{1}{216}

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Question 8

Time: 00:00:00
A pair of fair dice are rolled together, till a sum of either 5 or 7 is obtained. The probability that the sum 5 happens before sum 7 is

0.45

0.45

0.4

0.4

0.5

0.5

0.5

0.5

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Question 9

Time: 00:00:00
In the previous question, what is the probability of getting sum 7 before sum 5?

0.6

0.6

0.55

0.55

0.4

0.4

0.5

0.5

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Question 10

Time: 00:00:00
Numbers are selected at random one at a time, from the numbers 00, 01, 02,…., 99 with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, then the probability that E occurs at least 3 times is

\frac{97}{390625}

\frac{97}{390625}

\frac{98}{390625}

\frac{98}{390625}

\frac{97}{380626}

\frac{97}{380626}

\frac{97}{380625}

\frac{97}{380625}

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