One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?

Clearly n(S) = 52 and there are 16 face cards.
? P(E) = 16/52 = 4/13

An ordinary year has 365 days i,e. 52 weeks and 1 day. So the probability that this day is a Sunday is 1/7.

In a simultaneous throw of two dice
Simple Space = 6 x 6 = 36
Favorable cases are = (2, 6) (3, 5) (4, 4 ) (5, 3) (6, 2)
So, The required probability = 5/36

In tossing a coin 2 times the sample space is 4 i,e (H, H), (H, T), (T, H), (T, T)
(1) If A₁ denotes exactly one head
then A₁ = {(H, T) (T, H) }
So, P(A₁ ) = 2/4 = 1/2

(2) If A denotes at least one head
then A = {(H, T) (T, H) (H, H)}
? A = {(H, T) (T, H) (H, H )}
? P(A) = 3/4

The probability of absenting of the students in the class = 2/6 = 1/3
? The probability of missing his test = 1/5 x 1/3 = 1/15

Clearly, n (S) = 52, there are 4 kings and 4 queens
? P(E) = n (E) / n (S) = 8/52 = 2/13

There are 13 hearts and 3 more kings
? p (heart or a king ) = (13 + 3)/52 = 4/13
? P (neither a heart nor a king) = 1 - 4/13 = 9/13

First we place seven white balls at places market W.
W -- W --W --W --W -- W -- W

If we place three black balls at -- places. Then no two black balls will be placed adjacently.
Total No, of -- places = 8

? No. of favourable ways for black balls = ⁸C₃ = 8 x 7 x 6 / 1 x 2 x 3 = 56
Total no. of equally likely cases = 10! / 7!3!
= (10 x 9 x 8) / (1 x 2 x 3) = 15 x 8 = 120

? Reqd. Probability = 56 / 126 = 7/15

? Probability for 3 = (1, 2), (2, 1) = 2/36
? Probability for 5 = (1, 4), (2, 3), (3, 2), (4, 1)= 4/ 36
? Probability for 11 (5, 6), (6, 5) = 2/36

? Reqd . Probability = 2/36 + 4/36 + 2/36 = 8/36 = 2/9

P(M) = 1/4; P(W)= 1/3
? P (M) = 1 - 1/4 = 3/4
? P(W)= 1 - 1/3 = 2/3

Reqd. probability = P(M) P(W) = 3/4 x 2/3 = 1/2