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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

Given that P(A) = 1/4, and we know, and 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

Since,
A =  number > 3
A {4,5,6}
and B = number < 5
B = {1, 2, 3, 4}
∴ A∩B = {4}

∴ ⇒ 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

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 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

Let the events,
A = 1st aeroplane hit the target
B =2nd aeroplane hit the target
And their corresponding probabilities are Required Probability = (0.7)(0.2) + (0.7)(0.8)(0.7)(0.2)+ (0.7)(0.8)(0.7)(0.8)(0.7)(0.2) + .... The document Questions with Answers: Probability Notes - CAT is a part of CAT category.
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