Four boys and three girl stand in queue for an interview. The probability that they stand in alternate position is

First we find the probability that the plane is not hit
= (1 - 0.4) ( 1 - 0.3) (1 - 0.2) (1 - 0.1)
= 0.6 x 0.7 x 0.8 x 0.9 = 0.3024

? probability that the plane is hit = 1 - 0.3024
= 0.6976

Since, there are only two types of socks in the bag. so, if murari pick up 3 socks then certainly two of them are of same type. Thus this is a certain event.
Hence required probability = 1

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

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

Required probability = favorable number of cases/ total number of
=⁸P₅ / 8 ⁵ = 105/512

Total number of caps = 12
n(s) = ¹²c₁ = 12
Out of ( 2 blue + 1 yellow) caps, number of ways to pick one cap n(E) = ³c₁ = 3
? Required probability = p(E) = n (E) / n(s) = 3/12 = 1/4

Total number of ways of selection of 3 marbles out of 12
= n(S) = ¹²C₃ = 220
Total number of favorable events = n(E)
= ³C₃ + ⁴C₃ = 1 + 4 = 5
? Required probability
= 5/220 = 1/44

Required probability = 1- probability that all the girls sit together
= 1 - 1/42 = 41/42

Required probability = 1- probability that all the boys sit together
= 1- 1/42 = 41/42