A , B, C try to hit a target simultaneously but independently. Th… - Vidyadip

MCQ

$A , B, C$ try to hit a target simultaneously but independently. Their respective probabilities of hitting targets are $\frac{3}{4},\frac{1}{2},\frac{5}{8}$. The probability that the target is hit by $A$ or $B$ but not by $C$ is

✓
$21/64$
B
$7/8$
C
$7/32$
D
$9/64$

✓

Answer

Correct option: A.

$21/64$

a
$P(\text { A or } B \text { but not by } C)=P((A \cup B) \cap \bar{C})$

$=P(A \cup B) \times P(\bar{C})$

$=[\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})] \times \mathrm{P}(\overline{\mathrm{C}})$

$=$ $\left[\frac{3}{4}+\frac{1}{2}-\frac{3}{4} \times \frac{1}{2}\right] \times \frac{3}{8}=\left(\frac{6+4-3}{8}\right) \times \frac{3}{8}=\frac{21}{64}$

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 "MCQ" from 14. probability→14. probability — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\mathop {\lim }\limits_{x \to 0} \,\frac{{{e^x} - x - 1}}{{{x^2}}}$ is

Let $A _{1}, A _{2}, A _{3}, \ldots \ldots$ be an increasing geometric progression of positive real numbers. If $A _{1} A _{3} A _{5} A _{7}=\frac{1}{1296}$ and $A _{2}+ A _{4}=\frac{7}{36}$, then, the value of $A _{6}+ A _{8}+ A _{10}$ is equal to

Mathematical Induction is the principle containing the set.

The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is

For $x \in R$, then number of real roots of the equation $3 x^2-4\left|x^2-1\right|+x-1=0$ is. . . . . .

If the mean of $4, 7, 2, 8, 6$ and $a$ is $7$, then the mean deviation from the median of these observations is

If the complex number $z=2-i\left(2 \tan \frac{5 \pi}{8}\right)$ has modulus $r$ and argument $\theta$, then what are $(r, \theta)$ ?

If $\tan \alpha = {(1 + {2^{ - x}})^{ - 1}},$ $\tan \beta = {(1 + {2^{x + 1}})^{ - 1}}$, then $\alpha + \beta $ equals

One card is drawn from a pack of 52 cards. The probability of getting a jack card is:

${x^2} + x + 1 + 2k\,({x^2} - x - 1) = 0$is a perfect square for how many values of $k$