Top 50 Most Repeated PROBABILITY PYQs | JEE MAINS
A curated collection of the most important questions from PROBABILITY, fully solved with step-by-step concepts to prepare for JEE MAINS.
A curated collection of the most important questions from PROBABILITY, fully solved with step-by-step concepts to prepare for JEE MAINS.
Total number of balls = 5 + 8 + 7 = 20. Number of non-white balls = 5 (red) + 7 (black) = 12. So, P(not white) = $\frac{12}{20}$. This simplifies to $...
Read Full Step-by-Step Solution →After removing one red, 2 red and 2 green remain. P(green) = 2/4 = 1/2....
Read Full Step-by-Step Solution →This is a binomial distribution with $n=6$, $p=0.5$, $k=4$. Use formula: $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$. So $P(X=4) = \binom{6}{4} (0.5)^4 (0...
Read Full Step-by-Step Solution →Use P(A∪B) = P(A) + P(B) - P(A)P(B) for independent events....
Read Full Step-by-Step Solution →Step 1: Recall the formula for the mean of a binomial distribution, which is $np$.,Step 2: Recall the formula for the variance of a binomial distribut...
Read Full Step-by-Step Solution →Total outcomes = 36. Favorable outcomes for sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 cases. So, probability = $\frac{6}{36} = \frac{1}{6}$....
Read Full Step-by-Step Solution →Even numbers on a die are {2,4,6} → P(A)=3/6=1/2. Complement probability =1−1/2=1/2....
Read Full Step-by-Step Solution →Even numbers on a die are {2,4,6} (3 outcomes). The complement (odd numbers) also has 3 outcomes. Probability = 3/6 = 1/2....
Read Full Step-by-Step Solution →Prime numbers on a die: 2, 3, 5 → 3 outcomes. P = 3/6 = 1/2....
Read Full Step-by-Step Solution →Using the binomial formula P = C(5,3)·(0.4)³·(0.6)² = 10·0.064·0.36 = 0.2304....
Read Full Step-by-Step Solution →For a binomial distribution, mean $ = np = 8 $, variance $ = np(1-p) = 4 $. Dividing, $ \frac{np}{np(1-p)} = \frac{8}{4} \Rightarrow \frac{1}{1-p} = 2...
Read Full Step-by-Step Solution →Use binomial distribution: $P(X=3) = \binom{5}{3} \left(\frac{1}{2}\right)^5 = \frac{10}{32} = \frac{5}{16}$....
Read Full Step-by-Step Solution →Experimental probability is the ratio of observed favorable outcomes to total trials. As the number of trials grows, the law of large numbers ensures ...
Read Full Step-by-Step Solution →Theoretical probability of drawing a red ball is \(\frac{3}{10}=0.3\). Experimental probability is \(\frac{12}{40}=0.3\). Since both values are equal,...
Read Full Step-by-Step Solution →For a Poisson distribution with mean \(\lambda = 3\), \(P(X=2)=\frac{e^{-\lambda}\lambda^{2}}{2!}=e^{-3}\frac{9}{2}=4.5e^{-3}\approx0.224\)....
Read Full Step-by-Step Solution →Total ways to choose 2 balls from 12 is $\binom{12}{2}=66$. Same‑colour selections: red $\binom{5}{2}=10$, blue $\binom{4}{2}=6$, green $\binom{3}{2}=...
Read Full Step-by-Step Solution →Total ways to choose 2 balls: $\binom{12}{2}=66$. Same‑colour ways: $\binom{3}{2}+\binom{4}{2}+\binom{5}{2}=3+6+10=19$. Probability =
Mean = $np = 4$, Variance = $npq = 3$. Solving gives $q = \frac{3}{4}$, so $p = \frac{1}{4}$, $n = \frac{4}{1/4} = 16$....
Read Full Step-by-Step Solution →The coin can give 0 (tails) or 1 (heads). To get total 7, we need die = 7 (impossible) with heads = 0, or die = 6 with heads = 1. Only one favorable o...
Read Full Step-by-Step Solution →Step 1: Use the binomial distribution formula to find the probability that exactly $r$ successes occur in $n$ trials.,Step 2: Simplify the expression ...
Read Full Step-by-Step Solution →Only even prime is 2. One outcome out of six ⇒ $\frac{1}{6}$....
Read Full Step-by-Step Solution →This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Probability....
Read Full Step-by-Step Solution →Total number of balls = 5 + 8 + 7 = 20. Number of non-white balls = 5 (red) + 7 (black) = 12. So, P(not white) = $\frac{12}{20}$. This simplifies to $...
Read Full Step-by-Step Solution →After removing one red, 2 red and 2 green remain. P(green) = 2/4 = 1/2....
Read Full Step-by-Step Solution →This is a binomial distribution with $n=6$, $p=0.5$, $k=4$. Use formula: $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$. So $P(X=4) = \binom{6}{4} (0.5)^4 (0...
Read Full Step-by-Step Solution →Use P(A∪B) = P(A) + P(B) - P(A)P(B) for independent events....
Read Full Step-by-Step Solution →Step 1: Recall the formula for the mean of a binomial distribution, which is $np$.,Step 2: Recall the formula for the variance of a binomial distribut...
Read Full Step-by-Step Solution →Total outcomes = 36. Favorable outcomes for sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 cases. So, probability = $\frac{6}{36} = \frac{1}{6}$....
Read Full Step-by-Step Solution →Even numbers on a die are {2,4,6} → P(A)=3/6=1/2. Complement probability =1−1/2=1/2....
Read Full Step-by-Step Solution →Even numbers on a die are {2,4,6} (3 outcomes). The complement (odd numbers) also has 3 outcomes. Probability = 3/6 = 1/2....
Read Full Step-by-Step Solution →Prime numbers on a die: 2, 3, 5 → 3 outcomes. P = 3/6 = 1/2....
Read Full Step-by-Step Solution →Using the binomial formula P = C(5,3)·(0.4)³·(0.6)² = 10·0.064·0.36 = 0.2304....
Read Full Step-by-Step Solution →For a binomial distribution, mean $ = np = 8 $, variance $ = np(1-p) = 4 $. Dividing, $ \frac{np}{np(1-p)} = \frac{8}{4} \Rightarrow \frac{1}{1-p} = 2...
Read Full Step-by-Step Solution →Use binomial distribution: $P(X=3) = \binom{5}{3} \left(\frac{1}{2}\right)^5 = \frac{10}{32} = \frac{5}{16}$....
Read Full Step-by-Step Solution →Experimental probability is the ratio of observed favorable outcomes to total trials. As the number of trials grows, the law of large numbers ensures ...
Read Full Step-by-Step Solution →Theoretical probability of drawing a red ball is \(\frac{3}{10}=0.3\). Experimental probability is \(\frac{12}{40}=0.3\). Since both values are equal,...
Read Full Step-by-Step Solution →For a Poisson distribution with mean \(\lambda = 3\), \(P(X=2)=\frac{e^{-\lambda}\lambda^{2}}{2!}=e^{-3}\frac{9}{2}=4.5e^{-3}\approx0.224\)....
Read Full Step-by-Step Solution →Total ways to choose 2 balls from 12 is $\binom{12}{2}=66$. Same‑colour selections: red $\binom{5}{2}=10$, blue $\binom{4}{2}=6$, green $\binom{3}{2}=...
Read Full Step-by-Step Solution →Total ways to choose 2 balls: $\binom{12}{2}=66$. Same‑colour ways: $\binom{3}{2}+\binom{4}{2}+\binom{5}{2}=3+6+10=19$. Probability =
Mean = $np = 4$, Variance = $npq = 3$. Solving gives $q = \frac{3}{4}$, so $p = \frac{1}{4}$, $n = \frac{4}{1/4} = 16$....
Read Full Step-by-Step Solution →The coin can give 0 (tails) or 1 (heads). To get total 7, we need die = 7 (impossible) with heads = 0, or die = 6 with heads = 1. Only one favorable o...
Read Full Step-by-Step Solution →Step 1: Use the binomial distribution formula to find the probability that exactly $r$ successes occur in $n$ trials.,Step 2: Simplify the expression ...
Read Full Step-by-Step Solution →Only even prime is 2. One outcome out of six ⇒ $\frac{1}{6}$....
Read Full Step-by-Step Solution →This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Probability....
Read Full Step-by-Step Solution →Total number of balls = 5 + 8 + 7 = 20. Number of non-white balls = 5 (red) + 7 (black) = 12. So, P(not white) = $\frac{12}{20}$. This simplifies to $...
Read Full Step-by-Step Solution →After removing one red, 2 red and 2 green remain. P(green) = 2/4 = 1/2....
Read Full Step-by-Step Solution →This is a binomial distribution with $n=6$, $p=0.5$, $k=4$. Use formula: $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$. So $P(X=4) = \binom{6}{4} (0.5)^4 (0...
Read Full Step-by-Step Solution →Use P(A∪B) = P(A) + P(B) - P(A)P(B) for independent events....
Read Full Step-by-Step Solution →