Four fair sixsided dice are rolled. The probability that the sum of the results being 22 is . The value of X is ______
Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(AB) and P(BA) and respectively are
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You have to play three games with opponents A and B in a specified sequence. You win the series if you win two consecutive games. A is a stronger player than B. Which sequence maximizes your chance of winning the series?
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by 4?
The probability of throwing six perfect dices and getting six different faces is
There are 1000 balls in a bag, of which 900 are black and are white. I randomly draw 100 balls from the bag. What is the probability that the 100st ball will be black?
Two n bit binary strings, S_{1} and S_{2} are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to d is
A biased coin is tossed repeatedly. Assume that the outcomes of different tosses are independent and probability of heads is 2/3 in each toss. What is the probability of obtaining an even number of heads in tosses, zero being treated as an evennumber?
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise twothirds of the population the park, and give a correct answer to requests for directions with probability 3/4. The air of Kabrastan has an amnesaic quality however, and so the answers to repeated questions to tourists are independent, even if the question and the person are the same. If u ask a Kabrastani for directions, the answer is always wrong.
Suppose you ask a randomly chosen passer by whether the exit from the park is East or West. The answer is East. You then ask the same person again, and the reply is again East. What is the probability of East being correct?
Doctors A and B perform surgery on patients in stages III and IV of a disease. Doctor A has performed a 100 surgeries (on 80 stage III and 20 stage patients) and 80 out of her 100 patients have survived (78 stage III and 2 stage IV survivors). Doctor B has also performed 100 surgeries (on 50 stage III and 50 stage IV patients). Her success rate is (49 stage III survivors and 11 stage IV survivors). A patient has been advised that she is equally likely to besuffering from stage III or stage IV of this disease. Which doctor would you recommend to this patient and why?
An unbiased die is thrown n times. The probability that the product of numbers would be even is
If a fair coin is tossed four times. What is the probability that two heads and two tails will result?
Consider a sided die with all sides not necessarily equally likely such that probability of an even number is , probability of a multiple of and probability of . Given the above conditions, choose the strongest (most stringent) condition of the following that must always hold about , the probability of 5.
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is
The probability of three consecutive heads in four tosses of a fair coin is.
A probability density function on the interval [a,1] is given by 1/x^{2} and outside this interval the value of the function is zero.
The value of a is _________.
Consider the following experiment.
Step 1. Flip a fair coin twice.
Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop.
Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and stop.
Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places) ____________.
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?
A man has three cats. At least one is male. What is the probability that all three are male?
The probability that a number selected at random between 100 and 999 (both inclusive) will not contain the digit 7 is:
The 12 houses on one side of a street are numbered with even numbers starting at 2 and going up to 24. A free newspaper is delivered on Monday to 3 different houses chosen at random from these 12. Find the probability that at least 2 of these newspapers are delivered to houses with numbers strictly greater than 14.
You arrive at a snack bar and you can’t decide whether to order a lime juice or a lassi. You decide to throw a fair 6sided die to make the choice, as follows.
What is the probability that you end up ordering a lime juice?
Consider the function on three bits, maj : where maj if and only if be the probability that the output is 1 when each input is set to 1 independently with probability α. What is
If P and Q are two random events, then the following is TRUE:
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?
E_{1} and E_{2} are events in a probability space satisfying the following constraints:
The value of Pr(E_{1}), the probability of the event E_{1}, is
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is
A bag contains white balls and black balls. Two balls are drawn in succession. The probability that one of them is black and the other is white is:
The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is ______ .
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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?
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55 docs215 tests
