### Eamcet - Maths - Basic Probability

A man throws a die until he gets a number bigger than 3. The probability that he gets a 5 in the last throw is

A.  1/2

B.  1/3

C.  2/3

D.  3/5

Two cards aredrawn from a pack. The probability that one of them is  a club and the  other is not a club is

A.  1/36

B.  5/108

C.  26/51

D.  13/34

The letters of the word SUCCESS are arranged in a row at random. The probability that all S’s come together is

A.  3/35

B.  1/7

C.  3/7

D.  1/5

A five digit number is formed by using the digits 0, 1,2,3,4 and 5 without repetetion.The probability that the number is divisible by 6 is

A.  9/50

B.  10/39

C.  2/3

D.  1/16

A mapping is selected at random from the set of all mappings from the set A={1,2,3}in to B= {1,2,3,4}.The probability that the mapping selected is many to one is

A.  5/8

B.  3/8

C.  1/4

D.  24/64

5 digit numbers can be formed from the digits 0, 2,2,4,5. One number is selected at random.the probability that it is divisible by 5 is

A.  7/16

B.    1/16 1/16 1/26 7/26 1/16 1/26 7/26

C.  1/26

D.  7/26

One hundred cards are numbered from 1 to 100. The probability that a randomly chosen card has a digit 5 is

A.  1/100

B.  9/100

C.  19/100

D.  none

If a number x is selected from natural numbers 1 to 100,then the probability for x+100/x >29 is

A.  41/50

B.  47/50

C.  39/50

D.  37/50

If 1+3p/3, 1-2p/2are the probability of two mutually exclusive events, then p lies

A.  [-1/3,1/2]

B.  (-1/2,1/2)

C.  [-1/3,2/3]

D.  [-1/2,2/3]

A, B, C are three routes from the house to the office. On any day, the route selected by the officer is independent of the climate. On a rainy day, the probabilities of reaching the office late, through these routes are 1/25, 1/10, 1/4respectively. If a rainy day the officer is late to the office then the probability that the route to be B is

A.  5/6

B.  7/40

C.  29/40

D.  10/39

If three six faced dice are thrown together, then the probability that the sum of the numbers appearing on the dice is k(3≤k≤8)is

A.  (k-1)(k-2)/432

B.  k(k-1)/432

C.  k2/432

D.  none

If n positive integers are taken at random and multiplied together , the probability that the last digit of the product is 2,4,6 or 8 is

A.  5n-3n/5n

B.  4n+2n/5n

C.  3n-2n/5n

D.  3n-2n/4n

Five digit numbers can be formed from the digits 1,2,3,4,5. If one number is selected at random, the probability that it is an even number is

A.  4/7

B.  2/5

C.  7/16

D.  1/16

A bag contains four balls. Two balls are drawn and found them to be white. The probability that all the balls are white is

A.  1/2

B.  3/5

C.  1/4

D.  4/6

If 3 cards are drawn from a pack of cards, then the probability for the cards to be a king, a queen and a jack is

A.  52/52C3

B.  64/52C3

C.  78/52C3

D.  84/52C3

If the probability that A and B will die with in a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is

A.  p+q

B.  p+q-2pq

C.  p+q-pq

D.  p+q+pq

The eccentricity o the ellipse 9x2+16y2=576 is

A.  √7/2

B.  √5/2

C.  7/12

D.  √7/4

A bag contain 6 white and 4 black balls. A fair die is rolled and a number of balls equal to that appearing on the die is chosen from the bag at random. The probability that all the balls selected are white is

A.  1/5

B.  1/6

C.  1/7

D.  1/8

The vertex and focus of a parabola are (2, 1), (1, -1). Then the equation of the tangent at the vertex is

A.  x+2y-6=0

B.  x+2y-4=0

C.  x+2y-9=0

D.  x+2y-7=0

If one ticket is randomly selected from, tickets numbered from 1to 30 then the probabilitythat the numbered on the tickets i a multiple of 5 or 7 is

A.  1/3

B.  2/3

C.  4/3

D.  5/3

If the point of intersection of kx+4y+2=0, x-3y+5=0 lies on 2x+7y-3=0, then k=

A.  2

B.  3

C.  -2

D.  -3

A person has 3 shares in a lottery containing 2 prizes and 5 blanks. The chance of getting prize is

A.  3/10

B.  2/7

C.  5/7

D.  7/10

If P (A) =0.4, P (B) =0.5, P(C) =0.6, P (A∩B) =0.2, P (B∩C) =0.3, P (C∩A) =0.25, P (A∩B∩C) =0.1then P (AUBUC) =

A.  0.1

B.  0.9

C.  0.85

D.  0.8

The radical axis of the circles x2+y2-6x-4y-44=0 and x2+y2-14x-5y-24=0 is

A.  8x+y-30=0

B.  8x+y+20=0

C.  8x+3y-20=0

D.  8x+y-20=0

Bag A contains4 white, 3black balls.Bag B contains 3 white and 5 black balls.One ball is drawn from each bag .The probability that both are black is

A.  3/14

B.  15/56

C.  29/56

D.  4/5

The radius of the sphere x2+y2+z2-2x+4y-6z+7=0 is

A.  49

B.  5

C.  -7

D.  √7

The distance of (1, -2) from the common chord of x2+y2-5x+4y-2=0 and x2+y2-2x+8y+3=0 is

A.  2

B.  1

C.  0

D.  3

If the probability for A to fail in one exam is 0.2 and that of B is 0.3, then the probability that either A or B fails is

A.  0.14

B.  0.6

C.  0.44

D.  0.24

If 5 biscuits are distributed among 6 children, the probability that a particular child gets 4 sweets is

A.  10C4/ 610

B.  10C4*56/ 610

C.  10C4+56/ 610

D.  56/610

Three students A,B,C are to take part in a swimming competition. The probabilities of A ‘s winning or the probability of B’s winning of B’s winning is 3 times the probability of C’s winning. The probability of the event of either B or C to win is

A.  5/14

B.  3/7

C.  2/7

D.  4/7