Miscellaneous Question 56
In the given questions, two quantities are given. One as Quantity-I and the other is Quantity-II. You have to determine relationship between these two quantities and choose the appropriate options as given below :
(1) Quantity-I > II
(2) Quantity-I $<$ II
(3) Quantity-I $\leq$ II
(4) Quantity-I $\geq$ II
(5) Quantity-I = II (or) relationship cannot be established
- Consider the following probability cases.
Quantity-I: The chance of $X$ telling truth is $35 \%$ and the chance of Y telling truth is $75\%$. By what per cent both of them are likely to contradict each other in the same question?
Quantity-II: Two dice are thrown simultaneously. What is the probability of getting the sum of the numbers even?
Show Answer
Correct Answer: 56. (1)
Solution: 56. (1) Quantity I:
$\mathrm{P}(\mathrm{A})=\frac{35}{100}=\frac{7}{20}$ and
$\mathrm{P}(\mathrm{B})=\frac{75}{100}=\frac{3}{4}$
Contradiction $\rightarrow$ one lies and other speaks truth
So, the probability
$=\left(\left(\frac{7}{20}\right) \times\left(\frac{1}{4}\right)+\left(\frac{13}{20}\right) \times\left(\frac{3}{4}\right)\right)$
$=\frac{23}{40}=0.57$
Possible outcomes $=n(\mathrm{s})$
$=6 \times 6=36$
Let $\mathrm{E}$ be the events when sum is even.
So, $\mathrm{E}=\{(1,1),(1,3)(1,5)(2,2)$, $(2,4),(2,6), \ldots(6,2),(6,4)$, $(6,6)\} n(\mathrm{E})=18$
So, the required probability
$=\frac{18}{36}=1 / 2=0.5$
BETA
