A brother and sister appear for an interview against two vacant posts in an office. The probability of the brother's selection is 1/5th and that of the sister's selections is 1/3rd. What is the probability that one of them is selected?

Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
? Required probability = 2/3 x 3/4 = 1/2

Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3

Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
? Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8

Two cards can be drawn from a pack of 52 playing cards in ⁵²C₂ ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is ⁴C₂ ways, i.e 6 ways.
? The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221

A non-leap year has 365 days, each day repeats for 52 times with 1 day left
This one can be {Sun, Mon, Wed, Thu, Fri, and Sat}.
? p = 6/7

Total number of cards = 104
Total number of jacks = 8
? Probability for the jack in first draw = 8/104
and probability for the jack in second draw = 7/103
Since, both are independence events.
? Required probability = 8/104 x 7/103 = 7/1339

Probability of head or a tail on upper side of coin = 1/2
? Probability of getting same face on all three coins = 1/2 x 1/2 x 1/2
= 1/8

Total number of ways of selecting 1 card from 200 cards is ²⁰⁰C₁ ways.
Let E be an event of drawing a number which is a perfect cube.
E = {1, 8, 27, 64, 125 }
? P(E) = n(E) / n(S)
= ⁵C₁ / ²⁰⁰C₁ = 5/200 = 1/40

n(S) = 6 x 6 = 36
n(E) = (1, 2) (2, 1), (1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (3, 6) (4, 5) (5, 4) (6, 3) (6, 6) = 12
? P(E) = 12/36

Required probability = Probability of getting 2 tails + Probability of getting 1 tail + Probability of getting no tail.
= ⁸C₂ x 1/256 + ⁸C₁ x 1/256 + ⁸C₀ x 1/256
= 37/256