JEE Questions for Maths Probability Quiz 5

0%
1/72
0%
3/73
0%
5/72
0%
1/74
0%
1/73

In a Binomial distribution B(n, p = 1/4), if the probability of atleast one success is greater than or equal to 9/10, then n is greater than

0%
0%
2)
0%
0%

If X and Y are independent Binomial variates B(5, 1/and B(7, 1/2), then P(X + Y =is equal to

0%
35/47
0%
55/1024
0%
220/512
0%
11/204

If the random variable X takes the values x₁, x₂, x₃,...,x₁₀ with probabilities P(X = x₁) = ki, then the value of k is

0%
1/10
0%
1/4
0%
1/55
0%
7/12
0%
3/4

0%
m = σ2 = 2
0%
m = 1, σ2 = 2
0%
m = σ2 = 1
0%
m = 2, σ2 = 1

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is

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1/13
0%
3/13
0%
2/13
0%
None of these

The probability that a certain kind of component will survive a given shock test is 3/4. The probability that exactly 2 of the next 4 components tested survive is

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9/41
0%
25/128
0%
1/5
0%
27/128

A random variable X follows Binomial distribution with mean α and β. Then,

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0 < α < β
0%
0 < β < α
0%
α < 0 < β
0%
β < 0 < α

The mode of the Binomial distribution for which mean and standard deviation are 10 and √5 respectively, is

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7
0%
8
0%
9
0%
10

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

0%
1/729
0%
8/9
0%
8/729
0%
8/243

0%
7/12
0%
7/16
0%
3/4
0%
21/64

If X follows a Binomial distribution with parameters n = 100 and p = 1/3, then P(X = r) is maximum, when r is equal to

0%
16
0%
32
0%
33
0%
None of these

In a Binomial distribution, the mean is 15 and variance is 10. Then, parameter n is

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28
0%
16
0%
45
0%
25

A random variable X takes values 0, 1, 2, 3,... with probability P(X = x) = k(x +(1/5)^x, where k is a constant, then P(X =is equal to

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7/25
0%
18/25
0%
13/25
0%
19/25
0%
16/25

If the records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is

0%
8748 × 10-5
0%
1458 × 10-5
0%
1458 × 10-6
0%
41 × 10-6

0%
3
0%
1
0%
4
0%
2

At a telephone enquiry system, the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 min time intervals. The probability that there is atmost one phone call during a 10 min time period, is

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5/6
0%
6/55
0%
6/e5
0%
6/5e

0%
2/3
0%
4/9
0%
8/27
0%
16/81

An urn contains 4 white and 3 red balls. Three balls are drawn with replacement from this urn. Then, the standard deviation of the number of red balls drawn is

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6/7
0%
36/49
0%
5/7
0%
25/49

3 distinct integers are selected at random from 1, 2, 3,…, 20. The probability that the sum is divisible by 5 is

0%
0%
2)
0%
0%
None of these

A car is parked among N cars standing in a row, but not at either end. On his return, the owner finds that exactly r of the N places are still occupied. The probability that both the places neighbouring his car are empty is

0%
0%
2)
0%
0%
None of these

A fair coin is tossed 12 times. The probability that two heads do not occur consecutively is

0%
0%
2)
0%
0%
None of these

There are m persons sitting in a row. Two of these are selected at random. The probability that the two selected persons are not to-gether is

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0%
2)
0%
0%

A coin is tossed 30 times. For n = 1, 2,…, 20, the probability that 10 + n tosses will result in heads given that heads appeared at least m times is equal to

0%
0%
2)
0%
0%
None of these

A person throws two dice, one the common cube, and the other a regular tetrahedron, the number on the lowest face being taken in the case of tetrahedron. The probability that the sum of the numbers appearing on the dice is 6, will be

0%
0%
2)
0%
0%
None of these

If n positive integers are taken at random and multiplied together, then the probability that the last digit of the product is 2, 4, 6 or 8 is

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%

A bag has 13 red, 14 green and 15 black balls. The probability of getting exactly 2 blacks on pulling out 4 balls is p₁. Now the number of each colour ball is doubled and 8 balls are pulled out. The probability of getting exactly 4 blacks is p₂. Then

0%
0%
2)
0%
0%
None of these

Two persons A and B have respectively n + 1 and n coins, which they toss simultaneously. Then the probability that A will have more heads than B is

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%
None of these

On a chess-board if two squares are chosen, the probability that they have a side in common is

0%
0%
2)
0%
0%
None of these

If a number of two digits is formed with the digits 2, 3, 5, 7, 9 without repetition of digits. The probability that the number formed is 35, is

0%
0%
2)
0%
0%
None of these

In a game “odd man out” each of m ≥ 2 person tosses a coin to determine who will buy refreshments for the entire group. The odd man out is the one with a different outcome from the rest. The probability that there is a loser in any game is

0%
0%
2)
0%
0%
None of these

A bag contains n white and n red balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each pair consists of one white and one red ball is

0%
0%
2)
0%
0%
None of these

A contest consists of predicting the results (win, draw or defeat) of 10 football matches. The probability that one entry contains at least 5 correct answers is

0%
0%
2)
0%
0%
None of these

A pack of cards is counted with face downwards. It is found that one card is missing. One card is drawn and is found to be red. The probability that the missing card is red, is

0%
0%
2)
0%
0%
None of these

A point is selected at random from the interior of the circle. The probability that the point is closer to the centre than the boundary of the circle is

0%
0%
2)
0%
0%
None of these

A man firing at a distant target has 10% chance of hitting the target in one shot. The number of times he must fire at the target to have about 50% chance of hitting the target is

0%
10
0%
9
0%
7
0%
8

All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spade comes. The probability that the ace comes in the 4th draw is

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%
None of these

A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times, the probability that 2 hearts, 2 diamonds and 2 black cards are drawn is

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%
None of these

Ten pairs of shoes are in a closet. Four shoes are selected at random. The probability that there will be at least one pair among the four shoes selected is

0%
0%
2)
0%
0%
None of these

Numbers 1, 2, 3, …., 2n, n ∈ N are written down on 2n cards. One number is selected at random from these cards. If the probability of drawing a number ‘i’ is proportional to ‘i’, then the probability of drawing an odd number in one draw is

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0%
2)
0%
0%
None of these

Six girls are to enter a dance with 10 boys to form a ring so that every girl is between two boys. The probability that some specified boy remains between 2 boys is

0%
0%
2)
0%
0%
None of these

A chess game between Kamsky and Anand is won by whoever first wins a total of 2 games. Kamsky’s chance of winning, drawing or loosing a particular game are p, q, r. The games are independent and p + q + r = 1. The probability that Kamsky wins that match is