Probability (original) (raw)

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?

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

Consider a link with packet loss probability of 0.2. What is the expected number of transmissions it would take to transfer 200 packets given that the stop and wait protocol is used?

A class of 24 students occupies a classroom containing 4 rows of seats, with 7 seats in each row. If the students seat themselves randomly, what is the probability that the 5th seat in the 4th row is empty?

Two fair coins are tossed. It is known that at least one tail appears****.** What is the probability that both coins are tails?

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

Consider a finite sequence of random values _X = { __x_1, __x_2,..., _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.

If the difference between expectation of the square of a random variable (E[X²]) and the square of the expectation of the random variable (E[X])² is denoted by R, then?

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?

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

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