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# Questions with Answers: Probability - CSAT Preparation - UPSC

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 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
Hence Proved.

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 | CSAT Preparation - UPSC is a part of the UPSC Course CSAT Preparation.
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## FAQs on Questions with Answers: Probability - CSAT Preparation - UPSC

 1. What is probability and how is it related to statistics? Ans. Probability is a measure of the likelihood of an event occurring. It is closely related to statistics as it provides a foundation for analyzing and interpreting data. Probability allows us to quantify uncertainty and make informed decisions based on data.
 2. How is probability calculated? Ans. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability formula. In more complex scenarios, probability can be calculated using other methods such as the relative frequency approach or the subjective approach.
 3. What is the difference between theoretical probability and experimental probability? Ans. Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. It is determined by using formulas or probability rules. Experimental probability, on the other hand, is based on actual data collected through experiments or observations. It involves conducting experiments and recording the outcomes to determine the probability.
 4. What are independent and dependent events in probability? Ans. Independent events are those where the occurrence of one event does not affect the probability of the other event. For example, flipping a coin twice and getting heads on the first flip does not impact the probability of getting heads on the second flip. Dependent events, on the other hand, are events where the occurrence of one event affects the probability of the other event. For example, drawing cards from a deck without replacement.
 5. How can probability be applied in real-life situations? Ans. Probability has numerous applications in real-life situations. It is used in weather forecasting, risk assessment, insurance, gambling, sports predictions, stock market analysis, and many other areas. By understanding and applying probability, we can make informed decisions and predictions based on the likelihood of different outcomes.

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