Probability

Question 1

Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

• 8 / (2e³)
• 9 / (2e³)
• 17 / (2e³)
• 26 / (2e³)

Question 2

Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?

• 10/21
• 5/12
• 2/3
• 1/6

Question 3

Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = −1 and +1 are

• 0 and 0.5
• 0 and 1
• 0.5 and 1
• 0.25 and 0.75

Question 4

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

• 1/3
• 1/4
• 1/2
• 2/3

Question 5

Consider a finite sequence of random values X = { x₁, x₂,..., x_n}. Let μ_x be the mean and σ_x be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as y_i = a*x_i + b, where a and b are positive constants. Let μ_y be the mean and σ_y be the standard deviation of this sequence. Which one of the following statements is INCORRECT?

• Index position of mode of X in X is the same as the index position of mode of Y in Y.
• Index position of median of X in X is the same as the index position of median of Y in Y.
• μ_y = aμ_x+b
• σ_y = aσ_x+b

Question 6

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process.This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

• pq + (1 - p)(1 - q)
• (1 - q) p
• (1 - p) q
• pq

Question 7

What is the probability that divisor of 10⁹⁹ is a multiple of 10⁹⁶?

• 1/625
• 4/625
• 12/625
• 16/625

Question 8

An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?

• 0.453
• 0.468
• 0.485
• 0.492

Question 9

Consider a 3 game tournament between two teams. Assume that every game results in either a win or loss. The team that wins two or more games wins the series. The probability for wining the first game for both teams is 1/2. The probability for a team to win a game after a win is 2/3. The probability of wining a game after a loss is 1/3. Note that the effect of only previous game is considered. What is the probability for a team to win the series after loosing first game.

• 1/9
• 1/6
• 2/9
• 1/3

Question 10

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

• 0.24

• 0.36

• 0.4

• 0.6