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Questions with Answers: Probability Notes - CAT

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Q.1. If 4 whole numbers taken at random are multiplied together show that the chance that the last digit in the product is 1,3,7, or 9 is 16/625.

If the last digit is 1,3,7,9 in the product then we can only select numbers
whose last digit is 1,3,7 or 9 from 0,1,2,.....9
Probability that a selected number  ends with 1,3,7 or 9  = 4/10 = 2/5
Probability of selecting four such numbers = (2/5)= 16/625



Q.2. It is given that the events A and B are such that P(A) = 1/4, P(A|B) = 1/2 and P(B|A) = 2/3. Then P(B|A) = 2/3. Then P(B) is
(a) 1/2 
(b) 1/6 
(c) 1/3 
(d) 2/3

Correct Answer Option (c)
Given that P(A) = 1/4,
Questions with Answers: Probability Notes - CATand Questions with Answers: Probability Notes - CAT

we know, 

Questions with Answers: Probability Notes - CAT

and Questions with Answers: Probability Notes - CAT

Now, substitute the values in the formula, we get

(2/3) = P(B∩A)/ (1/4)

P(B∩A) = (2/3). (1/4)

P(B∩A) = 1/6

Substitute the values in (1), we get

P(A/B) = P(A∩B)/ P(B)

(1/2) = (1/6)/ P(B)

P(B) = (1/6). (2/1)

P(B) = 1/3


Q.3. 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 (AUB) is
(a) 2/5 
(b) 3/5 
(c) 0 
(d) 1

Correct Answer Option (d)
Since,
A =  number > 3
A {4,5,6}
and B = number < 5
B = {1, 2, 3, 4}
∴ A∩B = {4}

∴ Questions with Answers: Probability Notes - CAT

⇒ Questions with Answers: Probability Notes - CAT


Q.4. A pair of fair dice is thrown independently three times. The probability of getting a total of exactly 9 twice is
(a) 1/729
(b) 8/9
(c) 8/729
(d) 8/243

Correct Answer Option (d)
When two dice are thrown, the total number of sample space is 36
Probability of getting a total of 9 in a single throw
4/36 = 1/9
Hence, the probability of getting a score of exactly 9 twice
Questions with Answers: Probability Notes - CAT


Q.5. Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is
(a) 0.06 
(b) 0.14 
(c) 0.32 
(d) 0.7

Correct Answer Option (c)
Let the events,
A = 1st aeroplane hit the target
B =2nd aeroplane hit the target
And their corresponding probabilities are
Questions with Answers: Probability Notes - CATRequired ProbabilityQuestions with Answers: Probability Notes - CAT= (0.7)(0.2) + (0.7)(0.8)(0.7)(0.2)+ (0.7)(0.8)(0.7)(0.8)(0.7)(0.2) + ....Questions with Answers: Probability Notes - CAT

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