- In a cycle race there are 5 persons named as J,K,L,M,N participated for 5 positions. How many number of ways can M finishes always before N?

A. 20

B. 36

C. 55

D. 60 - A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?

A. 1/455

B. 2/455

C. 4/455

D. 1/91 - The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?

A. 12/35

B. 15/35

C. 18/35

D. 21/35 - If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is:

A. 19/52

B. 17/52

C. 4/13

D. 5/13 - Three 6 faced dice are thrown together. The probability that all the three show the same number on them is:

A. 1/64

B. 1/36

C. 5/9

D. 5/12 - A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?

A. 17/91

B. 33/91

C. 51/91

D. 65/91 - Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is:

A. 13/21

B. 10/19

C. 11/15

D. Cannot be determined - 10 books are placed at random in a shelf. The probability that a pair of books will always be together is:

A. 1/10

B. 1/5

C. 3/10

D. 9/10 - The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is:

A. 0.4869

B. 0.5834

C. 0.5904

D. 0.6234 - Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A. 1/2

B. 2/5

C. 8/15

D. 9/20

Total number of ways in which 5 persons can finish is 5! = 120 (there are no ties)

Now, in half of these ways M can finish before N

Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.

Probability that all the three marbles picked at random are blue = 3C

If both agree stating the same fact, either both of them speak truth or both speak false.

Probability = 3/5 * 4/7 + 2/5 * 3/7

= 12/35 + 6/35 = 18/35

P(SuK) = P(S) + P(K) - P(SnK), where S denotes spade and K denotes king.

P(SuK) = 13/52 + 4/52 - 1/52 = 4/13

If all 3 numbers have to be same; basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number.

Further the three dice can fall in 6 * 6 * 6 = 216 ways

Hence the probability is 6/216 = 1/36

Given that there are 3 blue marbles, 4 red marbles, 6 green marbles and 2 yellow marbles.

When 4 marbles are picked at random, then the probability that none is blue is = 12C

=>(12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91

There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.

10 books can be rearranged in 10! ways

Consider the 2 books taken as a pair then, number of favourable ways of getting these two books together is 9! 2!

Required probability = 1/5

P(winning prize atleast on one ticket)

= 1 - P('Losing on all tickets')

= 1 - (0.8)^4 = (1 + (0.8)^2)(1 - (0.8)^2)

= (1.64)(0.36) = 0.5904

Here, S = {1, 2, 3, 4, ...., 19, 20}

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}

P(E) = n(E)/n(S) = 9/20

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