If The Papers Of 4 Students Can Be Checked By Any One Of The 7 Teachers, Then The Probability That All The 4 Papers Are Checked By Exactly 2 Teachers Is

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Question

If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is

Solution

Correct option is

6/49

The total number of ways in which papers of 4 students can checked by seven teachers is 74.

The number of ways of choosing two teachers out of 7 is  the number of ways in which they can check four papers is 24. But this includes two ways in which all the papers will be checked by a single teacher. Therefore, the number of ways in which 4 papers can be checked by exactly two teachers is 24 – 2 = 14.

∴ the number of favorable ways

                                                    

Thus,   the required probability = 

Testing

SIMILAR QUESTIONS

Q1

A bag contains a white and b black balls. Two players, A and B alternate ydraw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, the ratio ab is

Q2

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non – zero is

Q3

A fair coin is tossed 100 times. The probability of getting tails an odd number of times is

Q4

One hundred identical coins, each with probability of head are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is

Q5

Suppose X follows a binomial distribution with parameters n and p, where 0 < p < 1. If P (X = r)/P(X = n – r) is independent of n for every value ofr, then 

Q6

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is

Q7

For the three events AB and CP(exactly one of the events A or Boccurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p2, where 0 < p < 1/2. Then the probability of at least one of the three events AB and C occurring is

Q8

Nine identical balls are numbers 1, 2,…9. Are put in a bag. A draws a ball and gets the number a. the ball is put back the beg. Next B draws a ball gets the number b. The probability that a and b satisfies the inequality a – 2b + 10 > 0 is

Q9

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is then,

Q10

Let ABC, be three mutually independent events. Consider the two statements S1 and S2.

                        S1 : A and B ∪ C are independent

                        S2 : A and B ∩ C are independent

Then