Download App

Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability4 Marks
Question
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution.
✓

Answer

Total number of ways of selecting two numbers= 2C6 = 15
Values of x (larger of the two) can be 2, 3, 4, 5, 6
$\text{ P(x = 2) } = \frac{1}{15},\text{ P(x = 3)} = \frac{2}{15},\text{ P(x = 4)} = \frac{3}{15}$
$\text{P(x = 5)} = \frac{4}{15}\text{ and P(x = 6)} = \frac{5}{15}$
$\therefore$ Distribution can bewritten as
x:  2 3 4 5 6
P(x): $\frac{1}{15}\frac{2}{15}\frac{3}{15}\frac{4}{15}\frac{5}{15}$
x P(x): $\frac{2}{15}\frac{6}{15}\frac{12}{15}\frac{20}{15}\frac{30}{15}$
$\text{ Mean } = \sum\text{x}\text{ P(x)} = \frac{70}{15}= \frac{14}{3}.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write the values of 'a' for which the following distribution of probabilities becomes a probability distributioin:
$\text{X}=\text{x}_\text{i}:$ $-2$ $-1$ $0$ $1$
$\text{P}(\text{X}=\text{x}_\text{i}):$ $\frac{1-\text{a}}{4}$ $\frac{1+2\text{a}}{4}$ $\frac{1-2\text{a}}{4}$ $\frac{1+\text{a}}{4}$
→
If $\text{A}=\begin{bmatrix}1&2&0\\-2&-1&-2\\0&-1&1\end{bmatrix}$, find A-1, solve the system of linear equations x - 2y = 10, 2x - y - z = 8, -2y + z = 7
→
For each of the differential equations given in find the general solution:
$\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}-\text{x}+\text{xy}\cot\text{x}=0\ (\text{x}\neq0)$
→
A shopkeeper has 3 varieties of pens 'A', 'B' and 'C'. Meenu purchased 1 pen of each variety for a total of Rs 21. Jeevan purchased 4 pens of 'A' variety 3 pens of 'B' variety and 2 pens of 'C' variety for Rs 60. While Shikha purchased 6 pens of 'A' variety, 2 pens of 'B' variety and 3 pens of 'C' variety for Rs 70. Using matrix method, find cost of each variety of pen.
→
Evaluate the following:
$\int\sqrt{\frac{\text{a}+\text{x}}{\text{a}-\text{x}}}\text{dx}$
→
If $\sin^2\text{y}+\cos\text{xy}=\text{k},$ find $\frac{\text{dy}}{\text{dx}}$ at $\text{x}=1,\text{y}=\frac{\pi}{4}$
→
A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.
→
Find the angle between the lines whose direction cosines are given by the equations l + m + n = 0, l2 + m2 - n2 = 0.
→
$\text{Find} \frac{\text{dy}}{\text{dx}} \text{if (x}^{2} + \text{y}^2)^{2} = \text{xy.}$
→
Show that the differential equation (x + y) dy + (x - y) dx = 0, is homogenous and find the particular solution, given that y = 1 when x = 1.
→