If two fair dice are rolled then what is the conditional probability that the first dice lands on 6 given that the sum of numbers on the dice is 8 ?

$\frac{1}{3}$
$\frac{1}{4}$
$\frac{1}{5}$
$\frac{1}{6}$

12.
Two symmetric dice flipped with each dice having two sides painted red, two painted black, one painted yellow and the other painted white. What. is the probability that both land on the same colour ?

$\frac{3}{18}$

$\frac{5}{18}$

$\frac{2}{9}$

$\frac{1}{3}$

B.

$\frac{5}{18}$

$2 Side \to Red 2 Side \to Black 1 Side \to Yellow 1 Side \to White ∵ Total face in dice = 6 ∴ Required Probability = \frac{2}{6} \times \frac{2}{6} + \frac{2}{6} \times \frac{2}{6} + \frac{1}{6} \times \frac{1}{6} + \frac{1}{6} \times \frac{1}{6} = \frac{4}{36} + \frac{4}{36} + \frac{1}{36} + \frac{1}{36} = \frac{10}{36} = \frac{5}{18}$

13.

There are n socks in a drawer, of which 3 socks are red. If 2 of the socks are chosen randomly and the probability that both selected socks are red is $\frac{1}{2}$ , then what is the value of n ?

3
4
5
6

14.

Two cards are chosen at random from a deck of 52 playing cards. What is the probability that both of them have the same value ?

$\frac{1}{17}$
$\frac{3}{17}$
$\frac{5}{17}$
$\frac{7}{17}$

15.

A and B are two events such that A and B are mutually exclusive. If P(A) = 0.5 and P(B) = 0.6, then what is the value of P(A / B) ?

$\frac{1}{5}$
$\frac{1}{6}$
$\frac{2}{5}$
$\frac{1}{3}$

16.

What is the probability that an interior point in a circle is closer to the center than to the circumference ?

$\frac{1}{4}$
$\frac{1}{2}$
$\frac{3}{4}$
It cannot be determined

17.

If A and B are two events, then what is the probability of occurrence of either event A or event B ?

P(A) + P(B)
$P (A \cup B)$
$P (A \cap B)$
P(A)P(B)

18.

In a class, 54 students are good in Hindi only, 63students are good in Mathematics only and 41 students aregood in English only. There are 18 students who are goodin both Hindi and Mathematics. 10 students are good in all three subjects.

What is the number of students who are good in either Hindi or Mathematics but not in English ?

99
107
125
130

19.

In a class, 54 students are good in Hindi only, 63students are good in Mathematics only and 41 students aregood in English only. There are 18 students who are goodin both Hindi and Mathematics. 10 students are good in all three subjects.

What is the number of students who are good in Hindi and Mathematics but not in English ?

18
12
10
8

20.

A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance ?