Let A and B be independent events where 0 < P (A) < 1, 0 < P (B) < 1. Show that P (A U B)’ = P (A’) P (B’)

Let A and B be independent events where 0 < P (A) < 1, 0 < P (B) < 1. Show that P (A | B) = P (A)

A bag contains 5 white, 7 black, and 4 red balls; find the chance that three balls drawn at random are all white.

a) 1/12

b) 1/36

c) 1/56

d) 1/63

One of two events must happen; given that the chance of the one is two-thirds that of the other, find the odds in favour of the other.

a) 1 to 2

b) 2 to 3

c) 3 to 4

d) 4 to 5

Compare the chances of throwing 4 with one dice, 8 with two dice, and 12 with 3 dice.

a) 36:30:25

b) 25:30:36

c) 1:2:8

d) 2:7:15

In shuffling a pack of cards, four are accidently dropped; find the chance that the missing cards should be one from each suit.

a) 2/21825

b) 3/2185

c) 2197/20825

d) 4/20825

There are three works, one consisting of 3 volumes, one of 4, and the other of one volume. They are placed on a shelf at random; find the chance that volumes of the same works are all together.

a)

b)

c)

d)

In a hand at whist what is the chance that the 4 kings are held by a specified player?

a) 7/2183

b) 9/2324

c) 11/4165

d) 13/4328

There are m rupees and n ten nP.’s, placed at random in a line. Find the chance of the extreme coins being both ten nP.’s

a)  

b)  

c)  

d)  

In tossing a coin, find the chance of throwing head and tail alternately in 3 successive trials.

a)

b)

c)

d)

Two drawings, each of 3 balls, are made from a bag containing 5 white and 8 black balls, the balls not being replaced before the second trial: find the chance that the first drawing will give 3 white and the second 3 black balls.

a)

b)

c)

d)

A bag contains 5 white and 3 black balls, and 4 are successively drawn out and not replaced. What is the chance that they are alternately of different colours?

a)

b)

c)

d)

In three throws with a pair of dice, find the chance of throwing doublets at least once.

a)

b)

c)

d)

If two coins are tossed 5 times, what is the chance that there will be 5 heads and 5 tails?

a)

b)

c)

d)

If 8 coins are tossed, what is the chance that one and only one will turn up head?

a)

b)

c)

d)

A and B draw from a purse containing 3 rupees and 4nP.’s; find their respective chances of first drawing a rupee, the coins when drawn not being replaced.

a) ;

b) ;

c) ;

d) ;

If on an average 1 vessel in every 10 is wrecked, find the chance that out of 5 vessels expected 4 at least will arrive safely.

a)

b)

c)

d)

In four throws with a pair of dice, what is the chance of throwing doublets twice at least?

a)

b)

c)

d)

There are 9 coins in a bag, 5 of which are rupees and the rest are unknown coins of equal value; find what they must be if the probable value of the draw is 60nP.

a) 5 nP. coins

b) 10 nP. coins

c) 20 nP. coins

d) 25 nP. coins

A has 3 shares in a lottery in which there are 3 prizes and 6 blanks; B has 1 share in lottery in which there is 1 prize and 2 blanks; find A’s chance of success to B’s.

a) 16 to 7

b) 8 to 7

c) 7 to 8

d) 7 to 16

If the independent events A and B are such that 0 < P (A) < 1 and 0 < P (B) < 1 then

a) True

b) False