# Probability

12
 Question 1
A number p is chosen at random from the numbers [-3, 3]. What is the probability that value of p < 2
 A 3/7 B 5/7 C 4/7 D 1/7
Probability
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Question 1 Explanation:
Favorable/Total = -ve numbers/total number
 Question 2
A box contains 6 black, 5 brown and 2 yellow balls. If 2 balls are selected at random, what is the probability that both are black?
 A 4/23 B 5/26 C 7/26 D 8/15
Probability
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 Question 3
4 dices are thrown simultaneously. What is the probability that all the dices show the same number.
 A 1/216 B 1/36 C 4/216 D 4/36
Probability
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 Question 4
An urn contains 12 red and 18 white marbles. Two marbles are drawn without replacement one after another. What is the probability that first is red and second is white?
 A 16/145 B 9/32 C 36/145 D 5/32
Probability
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Question 4 Explanation:
Two marbles are drawn without replacement one after another, then the probability that first is red and second is white,
```= (12/30)*(18/29)
= (2/5)*(18/29)
= (2*18) / (5*29)
= 36 / 145 ```
So, option (C) is correct.
 Question 5
What is the probability that a number selected from numbers [1,30] is prime number?
 A 1/3 B 2/7 C 5/9 D 5/30
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 Question 6
A bag contains 21 balls numbered 1 to 21. two balls are drawn one after another without replacement. Find the probability that both balls are even numbered.
 A 3/14 B 2/3 C 6/9 D 1/8
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 Question 7
A 5 digit number is formed by using digits 1, 2, 3, 4 and 5 with no two digits same. What is the probability that the formed number is divisible by 4?
 A 1/5 B 4/5 C 3/5 D 1/4
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Question 7 Explanation:
To be divisible by 4, the number has to end with the last two digits forming a number divisible by 4. Since there are only 5 digits: 1, 2, 3, 4, 5. So, possible last two digits according to divisibility by 4: 12 24 32 52 For each of them we now have to put the remaining numbers in front: 3x2x1, therefore 6 combinations for each number set = 6x4 (we have 4 sets from above) = 24. So, required probability is: P = Number of desired outcomes / number of possible outcomes = 24 /(5*4*3*2*1) = 24 / (5!) = 24 / 120 = 1/5 So, option (A) is correct.
 Question 8
A box having 5 black and 3 brown flags. Another box having 4 black and 6 brown flags. If one flag is drawn from each box. Find the probability that both flags are of different color.
 A 21/40 B 10/19 C 3/8 D 3/10
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 Question 9
Ram speaks truth in 3/4 of cases and Shyam in 4/5 of cases. In what percent of cases while narrating the same event are they likely to contradict each other?
 A 35% B 25% C 20% D 40%
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 Question 10
What is the probability of getting a sum of 9 from two throws of a dice?
 A 1/3 B 1/6 C 1/9 D 1/12
Probability
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Question 10 Explanation:
Total number of outcomes = 6 * 6 = 36. Total number of favorable outcomes = (3, 6), (4, 5), (5, 4) (6, 3) = 4. Therefore, required probability = 4/36 = 1/9.
There are 19 questions to complete.
12
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