JEE Main Probability Practice Questions With Solutions

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text{th }}$i^{\text{th}\textrm{ }} roll than the number obtained in the $(i-1{)}^{\text{th }}$\left(\right. i - 1 \left.\right)^{\text{th}\textrm{ }} roll, $i=2,3$i = 2 , 3, is equal to

There are three bags $X,Y$X , Y and $Z$Z. Bag $X$X contains 5 one-rupee coins and 4 five-rupee coins; Bag $Y$Y contains 4 one-rupee coins and 5 five-rupee coins and Bag $Z$Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag $\mathrm{Y}$Y, is :

Let the sum of two positive integers be 24 . If the probability, that their product is not less than $\frac{3}{4}$\frac{3}{4} times their greatest possible product, is $\frac{m}{n}$\frac{m}{n}, where $\gcd (m,n)=1$gcd \left(\right. m , n \left.\right) = 1, then $n$n-$m$m equals

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :

A company has two plants $A$A and $B$B to manufacture motorcycles. $60\mathrm{\%}$60 \% motorcycles are manufactured at plant $A$A and the remaining are manufactured at plant $B.80\mathrm{\%}$B .80 \% of the motorcycles manufactured at plant $A$A are rated of the standard quality, while $90\mathrm{\%}$90 \% of the motorcycles manufactured at plant $B$B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If $p$p is the probability that it was manufactured at plant $B$B, then $126p$126 p is

The coefficients $\mathrm{a},\mathrm{b},\mathrm{c}$a , b , c in the quadratic equation $\mathrm{a}{x}^2+\mathrm{bx}+\mathrm{c}=0$a x^{2} + bx + c = 0 are from the set $\{1,2,3,4,5,6\}$\left{\right. 1 , 2 , 3 , 4 , 5 , 6 \left.\right}. If the probability of this equation having one real root bigger than the other is p, then 216p equals :

The coefficients $a,b,c$a , b , c in the quadratic equation $a{x}^2+bx+c=0$a x^{2} + b x + c = 0 are chosen from the set $\{1,2,3,4,5,6,7,8\}$\left{\right. 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 \left.\right}. The probability of this equation having repeated roots is :

If the mean of the following probability distribution of a radam variable $\mathrm{X}$X :

is $\frac{46}{9}$\frac{46}{9}, then the variance of the distribution is

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn $\mathrm{A}$A is :