Fatima and John appear in an interview for two vacancies for the … - Vidyadip

Question

Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima's selection is $\frac{1}{7}$ and that of John's selection is $\frac{1}{5}$. What is the probability that,
Only one of them will be selected?

✓

Answer

Given,
Probability of Fatima's (F) selection $=\frac{1}{7}$
$\text{P(F)}=\frac{1}{7}\Rightarrow\ \text{P}(\overline{\text{F}})=\frac{6}{7}$
Probability of John's (J) selection $=\frac{1}{5}$
$\text{P(F)}=\frac{1}{5}\Rightarrow\ \text{P}(\overline{\text{F}})=\frac{4}{5}$
P(Only one of them selected)
$=\text{P}\big((\text{F}\cap\overline{\text{J}})\cup(\overline{\text{F}}\cap\text{J})\big)$
$=\text{P}(\text{F}) \text{P}(\overline{\text{J}})+\text{P}(\overline{\text{F}})\text{P}(\text{J})$
$=\frac{1}{7}\times\frac{4}{5}+\frac{6}{7}\times\frac{1}{5}$
$=\frac{4+6}{35}$
$=\frac{10}{35}$
$=\frac{2}{7}$
Required probability $=\frac{2}{7}$

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 "2 Marks Questions" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following:
$\big[\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat{\text{j}}\hat{\text{k}}\hat{\text{i}}\big]+\big[\hat{\text{k}}\hat{\text{i}}\hat{\text{j}}\big]$

Determine whether or not the definition of $^*$ given below gives a binary operation. In the event that $^*$ is not a binary operation give justification of this. On $R,$ define $^*$ by $a ^* b = a + 4b^2$ Here, $Z^+$ denotes the set of all non$-$negative integers.

Find the equation of the plane passing through the following point:
(0, -1, 0), (3, 3, 0) and (1, 1, 1)

For the matrices, A and B, verify that (AB)′ = B′A′, where $A=\left[\begin{array}{c} {1} \\ {-4} \\ {3} \end{array}\right], B=\left[\begin{array}{ccc} {-1} & {2} & {1} \end{array}\right]$

Find adjoint of each of the matrix.
$\begin{bmatrix}1&2\\3&4\end{bmatrix}$

Evaluate the following integrals:
$\int\bigg\{\text{x}^2+\text{e}^{\log\text{x}}+\Big(\frac{\text{e}}{2}\Big)^\text{x}\bigg\}\text{dx}$

If $\text{A}=\begin{bmatrix}9&1\\7&8\end{bmatrix},\text{ B}=\begin{bmatrix}1&5\\7&12\end{bmatrix},$ find matrix C such that 5A + 3B + 2C is a null matrix.

Write the value of the determinant $\begin{vmatrix}2&3&4\\5&6&8\\6\text{x}&9\text{x}&12\text{x}\end{vmatrix}$

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$

If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.