CBSE 2025 · Region 2 · Set 1 · Q30 · 3 marks
A die with number $\displaystyle 1$ to $\displaystyle 6$ is biased such that $\displaystyle \mathrm{P}(2)=\frac{3}{10}$ and probability of other numbers is equal. Find the mean of the number of times number $\displaystyle 2$ appears on the dice, if the dice is thrown twice.Two dice are thrown. Defined are the following two events A and B: $\displaystyle \mathrm{A}=\{(x, \mathrm{y}): x+\mathrm{y}=9\}, \mathrm{B}=\{(x, \mathrm{y}): x \neq 3\}$, where $\displaystyle (x, \mathrm{y})$ denote a point in the sample space. Check if events A and B are independent or mutually exclusive.
A die with number $\displaystyle 1$ to $\displaystyle 6$ is biased such that $\displaystyle \mathrm{P}(2)=\frac{3}{10}$ and probability of other numbers is equal. Find the mean of the number of times number $\displaystyle 2$ appears on the dice, if the dice is thrown twice.
Two dice are thrown. Defined are the following two events A and B: $\displaystyle \mathrm{A}=\{(x, \mathrm{y}): x+\mathrm{y}=9\}, \mathrm{B}=\{(x, \mathrm{y}): x \neq 3\}$, where $\displaystyle (x, \mathrm{y})$ denote a point in the sample space. Check if events A and B are independent or mutually exclusive.
Marking-scheme solution
\[\mathrm{P}(2)=\frac{3}{10}, \mathrm{P}(\text { any other number })=1-\frac{3}{10}=\frac{7}{10}
\]
Let X represent the Random Variable "the number of $\displaystyle 2$'s".
Then $\displaystyle \mathrm{X}=0,1,2$
ProbabilityIndependent EventsApplyshort_answermedium
More from Probability
- Assertion: Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at…2023 · asked 3×
- A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances…2025 · asked 3×
- Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung…2026 · asked 3×
- The probability distribution of a random variable X is: where k is some unknown constant. The probability…2024 · asked 3×
- Recent studies suggest that roughly 12 % of the world population is left handed. Depending upon the parents,…2023 · asked 3×
- Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let…2022 · asked 3×
- Let X be a random variable which assumes values x 1, x 2, x 3, x 4 such that 2 P(X=x 1)=3 P(X=x 2)=P(X=x 3)=5…2022 · asked 3×
- The probability distribution of a random variable X is given below: (i) Find the value of k. (ii) Find P(1 ≤…2023 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.