Let A,B and C be three events such that the probability that exactly one of A and B occurs is (1−k), the probability that exactly one of B and C occurs is (1−2k), the probability that exactly one of C and A occurs is (1−k) and the probability of all A,B and C occur simultaneously is k2, where 0<k<1. Then the probability that at least one of A,B and C occur is:
Held on 20 Jul 2021 · Verified 6 Jul 2026.
greater than 81 but less than 41
greater than 21
greater than 41 but less than 21
exactly equal to 21
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:
The probability distribution of a random variable $X$ is given below : \(\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X & 4k & \dfrac{30}{7}k & \dfrac{32}{7}k & \dfrac{34}{7}k & \dfrac{36}{7}k & \dfrac{38}{7}k & \dfrac{40}{7}k & 6k \\ \hline P(X) & \dfrac{2}{15} & \dfrac{1}{15} & \dfrac{2}{15} & \dfrac{1}{5} & \dfrac{1}{15} & \dfrac{2}{15} & \dfrac{1}{5} & \dfrac{1}{15} \\ \hline \end{array}\) If $\mathrm{E}(\mathrm{X})=\frac{263}{15}$, then $\mathrm{P}(\mathrm{X}<20)$ is equal to :
Two distinct numbers $a$ and $b$ are selected at random from $1,2,3, \ldots, 50$. The probability, that their product $a b$ is divisible by 3, is
A data consists of $20$ observations $x_1, x_2, \ldots, x_{20}$. If $\sum_{i=1}^{20}(x_i + 5)^2 = 2500$ and $\sum_{i=1}^{20}(x_i - 5)^2 = 100$, then the ratio of mean to standard deviation of this data is:
From a month of $31$ days, $3$ different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to $\dfrac{a}{b}$, where $a,b \in \mathbb{N}$ and $\gcd(a,b)=1$, then $a+b$ is equal to ______
Work through every JEE Main Probability & Statistics PYQ, year by year.