List of top Mathematics Questions on Probability

The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that:
(i) target is hit
(ii) atleast one shot misses the target.

Choose a possible probability density function from the given functions:

The probability density function of a continuous random variable is \[ f(x)= \begin{cases} \dfrac35 e^{-3x/5}, & x>0 \\ 0, & x\le0 \end{cases} \] The mean of the distribution is

If \(Z\) is a standard normal variable, \[ P(Z>z_1)=\alpha, \] \[ P(Z<z_2)=\beta \] and \(z_2<z_1\), then a possible value of \[ P(z_2<Z<z_1) \] is

If 2 coins are tossed and 2 dice are thrown, probability of getting at least 1 head and sum at least 9 is

A card is drawn from 52 cards. If A = diamond, B = ace, probability that exactly one occurs is

If \( b \) and \( c \) are numbers chosen at random from the set \( \{1,2,3,\ldots,10\} \) with replacement, then the probability that the quadratic equation \[ x^2 + bx + c = 0 \] has real roots is:

A pair of dice is thrown independently \(3\) times. The probability of getting a total score of at least \(9\) twice, is:

Let \( E_1, E_2 \) and \( E_3 \) be mutually independent events. Statement I: \( E_1 \) and \( E_2 \cup E_3 \) are independent. Statement II: \( E_1 \) and \( E_2 \cap E_3 \) are independent. Which one of the following options is correct?

In a bolt factory, machines \(A\), \(B\), and \(C\) manufacture \(25\%\), \(35\%\), and \(40\%\) of the total output respectively. There is a chance of having \(5\%\), \(4\%\), and \(2\%\) defective bolts manufactured by \(A\), \(B\), and \(C\) respectively. If a bolt is drawn at random from the output, then the probability that it is defective is:

If \(E_1\) and \(E_2\) are two events of a sample space such that \(P(E_1)=0.8\), \(P(E_2)=0.7\) and \(P(E_1\cap E_2)\geq c\), then \(c=\)

If a 4-digit number is chosen from all possible 4-digit numbers, probability of getting exactly three odd digits and one even digit is

Let \[ S=\{2,3,5,7,11,13\} \] Consider all onto functions from \(S\) to \(S\). If function \(f\) is chosen randomly, probability that \[ f(3)>3f(2) \] is

From the set of numbers \[ \{1,2,3,4,5,6,7,8,9,10,11,12\}, \] two numbers are selected at random. The probability that the two numbers selected differ by a prime number is

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn. If the number is non-prime, the probability that it came from Box I is:

For a biased die, the probabilities for different faces are given by P(1)=0.1, P(2)=0.32, P(3)=0.21, P(4)=0.15, P(5)=0.05, P(6)=0.17. The die is tossed and it is known that either face 1 or 2 turned up. The probability that it is face 1 is:

Two symmetric cubical dice are rolled once. Match the items of Column-I with the items of Column-II. center tabular|l|l|l|l| 2|c|Column-I & 2c|Column-II
A & Probability that the numbers appearing are equal & I & 1/12
B & Probability that the numbers are all distinct & II & 5/36
C & Probability that the sum of numbers is 10 & III & 1/6
D & Probability that the sum of numbers is 6 & IV & 4/36
tabular center

A hunter is firing at a target. He has only 10% chance of hitting it in one round. The number of rounds he must fire in order to have at least 50% chance of hitting the target at least once, is

From a set containing four positive numbers and four negative numbers, four numbers are chosen at random and they are multiplied. The probability that the obtained product is positive is:

From a group of 10 men and 5 women, a four-member committee which includes at least one woman is to be formed. Then the probability for the committee thus formed to have more women than men is:

Three numbers are chosen at random from \{1, 2, ..., 10\}. The probability that the minimum of the chosen numbers is 3 or their maximum is 7, is

From a pack of 52 playing cards, one card was found missing. From the remaining cards, two cards are drawn at random and found to be spade cards. The probability that the missing card is a spade card is

The chance of rain on a day when an outdoor picnic is arranged is \(40\%\). If it rains, the chance that the picnic will be ‘good and enjoyable’ is \(30\%\). However, if it does not rain, the chance that the picnic will be ‘good and enjoyable’ is \(80\%\). The chance (in %) that it was raining on the day of picnic, given that the picnic was indeed ‘good and enjoyable’ is (in integer).

It is given that \(\text{Prob}(-1 \leq z \leq 1)=0.683\), \(\text{Prob}(-2 \leq z \leq 2)=0.954\), and \(\text{Prob}(-3 \leq z \leq 3)=0.997\), when \(z\) follows a standard normal distribution. If \(X\) follows a normal distribution with mean and variance as \(5\) and \(4\), respectively, then \(\text{Prob}(1 \leq X \leq 7)=\underline{}\) (rounded off to three decimal places).

In a year of \(366\) days, what is the chance that three persons have different birthdays?