Out of 13 applicants for a job, there are 5 women and 8 men It is desired to select 2 persons for the job, The probability that atleast one of the selected persons will be a woman, is

Required probability = P (A) x p (B)
= (1- 1/4) x (1- 1/6) = (3/4) x (5/6)
= 5/8

Total lottery tickets = 10000
Total prize in the lottery = 10
? Probability getting a prize
= 10/10000 = 1/1000

Now, probability of not getting a prize
= 1 - probability of getting a prize
= 1 - (1/1000)
= 999/1000

Required probability = P(A) x P(B)
= (1 - 1/4) x (1 - 1/3) = 3/4 x 2/3 = 1/2

Total number of ways
= n(s) = ⁶c₂ = 15
Favorable number of ways
= n(E) = ³C₁ x ³C₁= 9
? Required probability = 9/15 = 3/5

Total balls in the box = 5
Second red ball can be drawn in two ways
Case I. First ball is white and second ball is red.
Its probability = 3/5.2/4 = 6/20 = 3/10
Case II: First ball is red and second ball is red
Its probability = 2/5.1/4 = 2/20 = 1/10
Hence, reqd. probability
= 3/10 + 1/10 = 4/10 = 2/5

Total events = n (s) = 2⁵ = 32
n(E) of getting heads = 1
p(E) = 1/32
? n(E) = 1 - p(E) = 1 - 1/32 = 31/32

Let P(B) = x
Given, P(A?B) = 0.8 and P(A) = 0.3
? P(A) + P(B) - P(A?B) = 0.8
? P(A) + P(B) - P(A) P(B) = 0.8 {?A and B are independent}
? 0.3 + x - 0.3x = 0.8
? 0.7x = 0.5
? x = 5/7

Let the number of green marble = x
Then, Probability of getting a green marble
= ^xc₁ / ²⁴c₁ = 2/3
? x/24 = 2/3
? x = 16

Here, total balls are 14.
? Required probability = (³c₁ + ⁷c₁) / ¹⁴c₁
= (3 + 7)/14
= 10/14
= 5/7

Probability that trousers are not black = 2/3
Probability that shirts are not black = 3/4
Required robability = 2/3 x 3/4 = 1/2