None of the above implications holds

Occurrence of E ⇒ Occurrence of F

Occurrence of F ⇒ Occurrence of E

Non-occurrence of E ⇒ Non-occurrence of F

JEE Questions for Maths Probability Quiz 13

In a trail the probability of success is twice the probability of failure. In six trails the probability of at least four successes will be

0%
0%
2)
0%
0%

A probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs none will fuse after 150 days of use

0%
0%
2)
0%
0%

A dice is thrown 5 times then the probability that an even number will come up exactly 3 times is

0%
0%
2)
0%
0%

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%
0%
2)
0%
0%

Assuming that for a husband wife couple the chances of their child being a body or a girl a the same, the probability of their two children being a boy and a girl is

0%
0%
1
0%
0%

The probability that a student is not a swimmer is 1/5. What is the probability that out of 5 students, 4 are swimmers

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

An experiment succeeds twice as often as it fails. Find the probability that in 4 trails there will be at least three success

0%
0%
2)
0%
0%

The mean and variance of a binomial distribution are 6 and 4. The parameter n is

0%
18
0%
12
0%
10
0%
9

Five coins whose faces are marked 2, 3 are tossed. The chance of obtaining a total of 12 is

0%
0%
2)
0%
0%

A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is

0%
0%
2)
0%
0%

A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is

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

0%
0%
2)
0%
0%

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

0%
0%
2)
0%
0%

If two coins are tossed 5 times, then the probability of getting 5 heads and 5 tails is

0%
0%
2)
0%
0%

In a binomial distribution the probability of getting a success is ¼ and standard deviation is 3, then its mean is

0%
6
0%
8
0%
12
0%
10

A coin is tossed 10 times. The probability of getting exactly six heads is

0%
0%
2)
0%
0%

If a dice is thrown twice, the probability of occurrence of 4 at least once is

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

A dice is thrown 100 times and getting an even number is considered a success. The variance of the number of successes will be

0%
10
0%
25
0%
18
0%
11

A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is

0%
2
0%
3
0%
4
0%
5

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

One coin is thrown 100 times. The probability of coming tail in odd number

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

A coin is tossed 3 times. The probability of obtaining at least two heads is

0%
0%
2)
0%
0%

A dice is thrown two times. If getting the odd number is considered as success, then the probability of two successes is

0%
0%
2)
0%
0%

The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

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

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

A sample of 4 items is drawn at a random without replacement from a lot of 10 items containing 3 defective. If X denotes the number of defective items in the sample then P(0 < x

0%
0%
2)
0%
0%

A random variable X has the following probability distribution

0%
3 and 2
0%
3 and 1
0%
3 and √3
0%
2 and 1
0%
3 and √2

A fair coin is tossed n and number of times. If the probability of having at least one head is more than 90%, then n is greater than or equal to

0%
2
0%
3
0%
4
0%
5

For the binomial distribution (p + q)ⁿ whose mean is 20 and variance is 16, pair (n, p) is

0%
0%
2)
0%
0%

0%
Occurrence of E ⇒ Occurrence of F
0%
Occurrence of F ⇒ Occurrence of E
0%
Non-occurrence of E ⇒ Non-occurrence of F
0%
None of the above implications holds

A coin is tossed m + n times, where m ≥ n. The probability of getting at least m consecutive heads is

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

An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is

0%
0.25
0%
0.21
0%
0.16
0%
0.6976

A bag contains a white and b black balls. Two players A and B alternately draw a ball from the beg 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, then the ratio a:b is

0%
1:1
0%
1:2
0%
2:1
0%
None of these

0%
0%
2)
0%
0%

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

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

If P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09, P(A + B + C) ≥ 0.75 and P(BC) = x then

0%
0.23 ≤ x ≤ 0.48
0%
0.32 ≤ x ≤ 0.84
0%
0.25 ≤ x ≤ 0.73
0%
None of these

An unbiased coin I tossed. If the result is a head, a pair of unbiased dice is rolled and the number of obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4,..,12 is picked and the number on the card is noted. The probability that the noted number is either 7 or 8, is

0%
0.24
0%
0.244
0%
0.024
0%
None of these

Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of then will be alive next 30 years

0%
0%
2)
0%
0%

A rifle man is firing at a distant target and has only 10% chance of hitting it. The minimum number of round he must fire in order to have 50% chance of hitting it at least once is

0%
7
0%
8
0%
9
0%
6

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7^m + yⁿ is divisible by 5 equals

0%
0%
2)
0%
0%

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

0%
0%
2)
0%
0%

Two persons A and B take turn is throwing a pair of dice. The first person to throw 9 from both dice will be awarded the prize. If A throws first then probability that B wins the game is

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

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 minute time intervals. The probability that there is at the most one phone call during a 10 minutes time period is

0%
0%
2)
0%
0%

Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively

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

Cards are drawn one by one at random from a well shuffled full pack of 52 cards until two aces are obtained for the first time. If N is the number of cards required to be drawn, then P_r {N = n}, where 2 ≤ n ≤ 50, is