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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Determine whether the following operations define a binary operation on the given set or not:
$'\times _6'$ on $S = \{1, 2, 3, 4, 5\}$ defined by, $a \times _6 b =$ Remainder when ab is divided by $6.$

Let $S = \{a, b, c\}$ and $T = \{1, 2, 3\}.$ Find $F^{–1}$ of the following functions $F$ from $S$ to $T,$ if it exists:
$F = \{(a, 3), (b, 2), (c, 1)\}$

Define differentiability of a function at a point.

Which of the following graphs represents a one-one function?

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:

₹ 50
₹ 20
₹ 40

The number of attempts made in three villages X, Y and Z are given below:

	(i)	(ii)	(iii)
X	400	300	100
Y	300	250	75
Z	500	400	150

Find the total cost incurred by the organisation for three villages separately, using matrices.

Integrate the function in Exercise:
$\text{e}^\text{x}\Bigg(\frac{1}{\text{x}}-\frac{1}{\text{x}^2}\Bigg)$

Show that the following systems of linear equations has infinite number of solutions and solve:

Compute the products AB and BA whichever exists the following cases:
$\text{A}=\begin{bmatrix}1&-2\\2&3\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}$

Evaluate:
$\sin\Big(\tan^{-1}\text{x}+\tan^{-1}\frac{1}{\text{x}}\Big)\text{ for }\text{x}<0$

If x and y are connected parametrically by the equation x = a ($\theta$ – sin $\theta$), y = a (1 + cos $\theta$) without eliminating the parameter. Find $\frac{d y}{d x}$.