Probabilities of solving a specific problem independently by A an… - Vidyadip

Question

Probabilities of solving a specific problem independently by A and B are $\frac{1}{2} \text{and}\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that(i) the problem is solved (ii) exactly one of them solves the problem.

✓

Answer

Here P(A) = $\frac{1}{2}$ $\therefore$ P(Not A) = $\frac{1}{2}$

and P(B) = $\frac{1}{3}$ $\therefore$ P(Not A) = $\frac{2}{3}$

P(problem is solved) = 1 - P (problem is not solved)

= 1 - P(Not A) . P(Not B)

=$1-\frac{1}{2}\cdot\frac{2}{3}=\frac{2}{3}$

P(exactly one of them solves) =$\text{P(A)}\cdot\text{P}\overline{(B)}+\text{P(B)}\cdot\text{P}\overline{(A)}$

$=\frac{1}{2}\cdot\frac{2}{3}+\frac{1}{3}\cdot\frac{1}{2}$

$=\frac{1}{2}$.

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 "5 Marks Questions" 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

Consider $f: R_+\rightarrow [– 5, \infty )$ given by $f(x) = 9x^2 + 6x – 5.$ Show that f is invertible with $f^{-1}(\text{y})=\left(\frac{\Big(\sqrt{\text{y}+6}\Big)-1}{3}\right).$

Prove that:
$\cos^{-1}\frac{12}{13}=\sin^{-1}\frac{3}{5}=\sin^{-1}\frac{3}{5}=\sin^{-1}\frac{56}{65}$

Differentiate the following functions with respect to x:
$\sin^{-1}\Big\{\frac{\text{x}}{\sqrt{\text{x}^2+\text{a}^2}}\Big\}$

Evaluate the following integrals:
$\int\frac{1}{\sin\text{x}+\sin2\text{x}}\ \text{dx}$

Using the method of integration find the area bounded by the curve |x| + |y| = 1
[Hint: the required region is bounded by lines x + y = 1, x - y = 1, -x + y = 1 and -x - y = 11]

If $\text{A}=\begin{bmatrix}1&2&0\\3&-4&5\\0&-1&3\end{bmatrix},$ compute $A^2 - 4A + 3I_3$.

A manufacturer makes two types $A$ and $B$ of tea-cups. Three machines are needed for the manufacture and the time in minutes required for each cup on the machines is given below:

	Machines
	$I$	$II$	$III$
$A$	$12$	$18$	$6$
$B$	$6$	$0$	$9$

Each machine is available for a maximum of $6$ hours per day. If the profit on each cup $A$ is $75$ paise and that on each cup $B$ is $50$ paise, show that $15$ tea-cups of type $A$ and $30$ of type $B$ should be manufactured in a day to get the maximum profit.

Verify Rolle's theorem for the function $f ( x) = x^{2} - 5x + 4\text{ on} [ 1, 4].$

Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and food Q costs Rs 80/kg. Food P contains 3 units/kg of vitamin A and 5 units/kg of vitamin B while food Q contains 4 units/kg of vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.

Let N denote the set of all natural numbers and R be the relation on$\text{N} \times \text{N}$defined by $\text{(a, b) R (c, d)}$ if ad$\text{(b + c) = bc(a + d)}$. Show that R is an equivalence relation.