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If \( P(A\cup B)=0.6\text{ and }P(A\cap B)=0.2 \), then the probability of exactly one of the event occurs is ________.
If \(P(A)=0.5,\ P(B)=0.4\text{ and }P(A\cap B)=0.3\text{ then } P\left( \dfrac{A^\prime}{B^\prime} \right) \) is equal to______
Thr chances to fail in physics are \( 20\%\)and the chances to fail in Mathematics are \( 10\% \).
What are the chances to fail at least one subject?
A parent has two children. If one of them is a boy, then the probability that other is also a boy is __________.
If \(P(A)=P(B)=x\text{ and }P(A\cap B)=P(A^\prime\cap B^\prime)=\dfrac{1}{3}\), then \( x \) is equal to _________.
If \( A\text{ and } B \) are mutually exclusive with \( P(A)=\dfrac{1}{2}\ P(B)\text{ and }A\cup B=S\text{ (total sample space)} \), then \(P(A)\text{ is equal to} \) _______.
The probability that in the toss of two dice, we obtain the sum \( 7 \text{ or }11 \) is _________.
If events are independents and \( P(A)=\dfrac{1}{3},\ P(B)=\dfrac{1}{3}\text{ and }P(C)=\dfrac{1}{4} \), then \( P(A^\prime\cap B^\prime\cap C^\prime) \) is equal to _________.
Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is _________.
A coin and sixfaced die, both unbiased, are thrown simultaenously. The probability of getting a head on the coin and an odd number on the die is _________.
If \(A\text{ and }B \) are two independent events such that \( P(A)=\dfrac{1}{2}\text{ and }P(B)=\dfrac{1}{3}\text{ then }P(A^\prime\cap B^\prime)\) is equal to [/latex] _________.
The probability of getting at least one tail in \( 4 \) throws of a coin is _________.
Probability of getting one tail in throws of a coin
Probability of getting at least one tail in throws of a coin
Five persons \( A,B,C,D\text{ and }E \) are in queue of a shop. The probability that \( A\text{ and }E \) are always together is _________.
Sample Space
Favorable number of ways
Probability
A fair sixfaced die is rolled \( 12 \) times. The probability that each face turns up twice is equal to _________.
Number of ways that each face turns twice
Total number of ways each face appears
Required Probability
A poker hand consists of \( 5 \) cards drawn at random from a wellshuffled pack of \( 52 \) cards.
Then, the probability that a poker hands consists of a pair and a triple of equal face values (e.g. \(2 \) seven and \(3 \) kings or \(2 \) aces and \(3 \) queens, etc.) is______
A sixfaced unbiased dice is thrown twice and the sum of the numbers appearing on the upper face is observed to be \( 7 \).
The probability that the number \( 3 \) has appeared atleast once, is _________.
(the number appeared at least once)
There are \( 7 \) horses in a race, Mr. X selected \( 2 \) at random and bet on them.
The probability that Mr. X selected the winning horse is _______.
If \( n \) integers taken at random are multiplied together, then the probability that the last digit of the product is \( 1,3,7\text{ or }9 \) is _________.
Favorrable number of ways
Sample Space
The probability that a leap year will have only \( 52 \) Sunday is _________.
There are days or weeks and days in a leap year.
If the first day is Sunday, then there will be Sundays. From third day to seventh day we have only Sundays.
The probability is .
Probability of all \( 3 \)digit numbers having all the digits same is _________.
Tota number of digit number
Total number of digit number having all digits same
Probability of getting positive integral roots of the equation \( x^2n=0\) for the integers \( n \), \( 1 \leq n \leq 40 \) is _________.
Three randomly chosen non negative integers \( x,y\text{ and }z \) are found to satisfy the equation \( x+y+z=10 \). Then the probability that \( z \) is even is_____________.
If \( 12 \) identical balls are to be placed in \( 3 \) different boxes, then the probability that one of the boxes contains exactly \( 3 \) balls is __________.
We have mentioned that boxes are different and one particular box has balls.
Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is atleast one more that the number of girls ahead of her, is _________.
Total number of ways to arrange boys and girls are
Number of favorable cases
Probability
Three identical dice are rolled. The probability that the same number will appear on each of them is _________.
Total number of cars
The same number appear on each of them