A bit string of length four is generated at random. What is probability that it contains at least two consecutive 0 's given that first bit is 0?

In a group of 120 people: 65 eat Rice, 45 eat bread, 42 eat curd, 20 eat both Rice and bread, 25 eat both Rice and curd, 15 eat both bread and curd and 8 eat all three items. Which of the following is the number of people who eat at least one of the three items?

In a pack of 42 cards, 3 cards are chosen one after the other. Find the number of ways this can be done without replacement:

Let us assume a person climbing the stairs can take one stair or two stairs at a time. How many ways can this person climb a flight of eight stairs?

How many ways are there to assign 5 different jobs to 4 different employees if every employee is assigned at least 1 job?

There are three boxes. First box has 2 white, 3 black and 4 red balls. Second box has 3 white, 2 black and 2 red balls. Third box has 4 white, 1 black and 3 red balls. A box is chosen at random and 2 balls are drawn out of which 1 is write, and 1 is red. What is the probability that the ball balls came from first box?

A coin is tossed successively three times. Find the Probability (P), Event (E), Sample space (S) of getting exactly one head or two heads, where n is number of occurrences.
A. n(S) = 8 and n(E) = 4
B. n(E) = 6 and n(S) = 8
C. P(E) = 3 / 4
D. P(E) = 1 / 2
Choose the correct answer from the options given below:

40 software professionals were interviewed for a job. 25 knew PYTHON 20 knew JAVA and 7 knew neither language. How many knew both languages?

Match List - I with List – II.

List – I (Queries)	List – II (Probability)
A.	A bag contains 6 white and 4 red balls. Two balls are drawn at random. What is the chance, they will be the same colour?	I.	3/68
B.	In a pack of 52 cards, one card is drawn at random, what is the probability that it is either a king or a queen?	II.	14/68
C.	A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 1 red and 2 white balls?	III.	2/13
D.	A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random. Find the probability of 2 blue and 1 red balls?	IV.	7/15

Choose the correct answer from the options given below:

A bit string of length four is generated at random. What is probability that it contains at least two consecutive 0 's given that first bit is 0?

In a group of 120 people: 65 eat Rice, 45 eat bread, 42 eat curd, 20 eat both Rice and bread, 25 eat both Rice and curd, 15 eat both bread and curd and 8 eat all three items. Which of the following is the number of people who eat at least one of the three items?