Mathematics - Probability
Exam Duration: 45 Mins Total Questions : 30
a bag contains five white and three black balls. Four balls are drawn one by one without replacement. The probability that the balls are alternately of different colours, is
- (a)
\(\cfrac { 1 }{ 4 } \)
- (b)
\(\cfrac { 1 }{ 6 } \)
- (c)
\(\cfrac { 1 }{ 7 } \)
- (d)
\(\cfrac { 1 }{ 8 } \)
If A, B, C are events such that
Pr (A)=0.3,Pr (B)=0.4;Pr (C)=0.8
Pr (AB)=0.08,Pr (AC)=0.28,Pr (ABC)=0.09
If \({ P }_{ r }(A\cup B\cup C)\ge 0.75\),
Then Pr (BC) lies in the interval
- (a)
(0, 0.23)
- (b)
(0, 0.48)
- (c)
(0.23, 0.48)
- (d)
NONE OF THESE
A dice is rolled 20 times. The probability of obtaining 5 for the first time at the 20th throw is
- (a)
\(\cfrac { 1 }{ 6 } { \left( \cfrac { 5 }{ 6 } \right) }^{ 19 }\)
- (b)
\(\left( \cfrac { 5 }{ 6 } \right) { \left( \cfrac { 1 }{ 6 } \right) }^{ 19 }\)
- (c)
\(\left( \cfrac { 5 }{ 6 } \right) ^{ 20 }\left( \cfrac { 1 }{ 6 } \right) \)
- (d)
NONE OF THESE
A and B take turns in tossing a pair of dice. The first to get a throw of 7 wins. If A starts the game the chance of winning of A, is
- (a)
\(\cfrac { 6 }{11 } \)
- (b)
\(\cfrac { 5 }{11 } \)
- (c)
\(\cfrac { 1 }{11 } \)
- (d)
NONE OF THESE
Bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from the bag B is
- (a)
\(\cfrac { 5 }{ 9 } \)
- (b)
\(\cfrac { 4 }{ 9 } \)
- (c)
\(\cfrac { 25 }{ 52 } \)
- (d)
NONE OF THESE
A coin is tossed 2n times. The chance that number of times one gets head is not equal to the number of times one gets tail is
- (a)
\(\cfrac { (2n)! }{ (n!) } { \left( \cfrac { 1 }{ 2 } \right) }^{ 2n }\)
- (b)
\(1-\cfrac { (2n)! }{ (n!) } \)
- (c)
\(1-\cfrac { (2n)! }{ (n!) } { \left( \cfrac { 1 }{ { 4 }^{ n } } \right) }\)
- (d)
NONE OF THESE
If n biscuits be distributed at random among N beggers the chance that a particular beggar receives r(
- (a)
\(^{ n }{ C_{ r } }.\cfrac { { N }^{ n } }{ { (N-r) }^{ n-r } } \)
- (b)
\(^{ n }{ C_{ r } }.\cfrac { { (N-1) }^{ n-r } }{ { N }^{ n } } \)
- (c)
\(^{ n }{ C_{ r } }.\cfrac { { (N-1) } }{ { N }^{ N } } \)
- (d)
NONE OF THESE
It is given that the events A and B such that \(P(A)={1\over4}\), P(A/B)=\(1\over2\) and P(B/A)=\({2\over3}\). Then, P(B) is
- (a)
\(1\over2\)
- (b)
\(1\over6\)
- (c)
\(1\over3\)
- (d)
\(2\over3\)
A pair of fair dice is thrown independently three times. The probability of getting a score of exatly 9 twice is
- (a)
\(1\over729\)
- (b)
\(8\over9\)
- (c)
\(8\over729\)
- (d)
\(8\over 243\)
A boy is throwing stones at a target. The probability of hitting the target at any trial is \(\frac { 1 }{ 2 } \) . The probability of hitting the target 5th time at the 10th throw is
- (a)
\(\frac { 5 }{ { 2 }^{ 10 } } \)
- (b)
\(\frac { 63 }{ { 2 }^{ 9 } } \)
- (c)
\({^{10}c_5}\over{2^{10}}\)
- (d)
\({^{10}c_4}\over{2^{10}}\)
The probability of guessing correctly atleast 8 out of 10 answers on a true-false examination, is
- (a)
7/64
- (b)
7/128
- (c)
45/1024
- (d)
175/1024
Two persons each makes a single throw with a pair of dice. The probability that the throws are unequal is given by
- (a)
\(\frac { 1 }{ { 6 }^{ 3 } } \)
- (b)
\(\frac { 73 }{ { 6 }^{ 3 } } \)
- (c)
\(\frac { 51 }{ { 6 }^{ 3 } } \)
- (d)
none of these
A box contains tickets numbered 1 to 20. 3 tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7, is
- (a)
7/20
- (b)
1-(7/20)3
- (c)
2/10
- (d)
none of these
A bag contains 14 balls of two colours, the number of balls of each colour being the same. 7 balls are drawn at random one by one. The ball in hand is returned to the bag before each new drawn. If the probability that at/east 3 balls of each colour are drawn is p, then
- (a)
\(p>\frac { 1 }{ 2 } \)
- (b)
\(p=\frac { 1 }{ 2 } \)
- (c)
\(p<1\)
- (d)
\(p<\frac { 1 }{ 2 } \)
Two distinct numbers are selected at random from the first twelve natural numbers. The probability that the sum will be divisible by 3 is
- (a)
1/3
- (b)
23/66
- (c)
1/2
- (d)
none of these
If A and B are independent events such that 0< P(A) < 1, 0 P(B) < 1, then
- (a)
A, B are mutually exclusive
- (b)
A and \(\overline { B } \) are independent
- (c)
\(\overline { A } \overline { B } \) are independent
- (d)
P(A/B) + P(A/B) = 1
Three six faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k(3\(\le \)k\(\le \)8) is
- (a)
\(\frac { (k-1)(k-2) }{ 432 } \)
- (b)
\(\frac { k(k-2) }{ 432 } \)
- (c)
\(^{ k-1 }{ { C }_{ 2 } }\times \frac { 1 }{ 216 } \)
- (d)
\(\frac { k^{ 2 } }{ 432 } \)
The letters of the word PROBABILITY are written down at random in a row. Let E1 denotes the event that two I's are together and E2 denotes the event that two B's are together, then
- (a)
\(P({ E }_{ 1 })=P({ E }_{ 2 })=\frac { 2 }{ 11 } \)
- (b)
\(P\left( { E }_{ 1 }\cap { E }_{ 2 } \right) =\frac { 2 }{ 55 } \)
- (c)
\(P\left( { E }_{ 1 }\cup { E }_{ 2 } \right) =\frac { 18 }{ 55 } \)
- (d)
\(P({ E }_{ 1 }/{ E }_{ 2 })=\frac { 1 }{ 5 } \)
If a particular experiment be given n (a finite) independent trials.
If the probability of success in one trial (say) p
\(\therefore\) We get probability of failure, q = (1 - p)
The probability of r success in n trials =nCrprqn-r
When two dice are thrown n number of times, the probability of getting atleast one double six is greater than 99%. then the least value of n is (Given log 35 = 1.5441, log 36 = 1.5563)
- (a)
150
- (b)
154
- (c)
160
- (d)
164
If A and B are two events, then the set (A \(\cap \) B) denotes the event
- (a)
A or B
- (b)
A and B
- (c)
only A
- (d)
only B
Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment.
A: "the sum is even".
B: "the sum is a multiple of3".
C: "the sum is less than 4".
D: "the sum is greater than 11".
Which pair of these events is mutually exclusive?
- (a)
A and B
- (b)
B and C
- (c)
C and D
- (d)
A and C
A die is thrown three times and the sum of three numbers obtained is 15. The probability of first throw being 4, is
- (a)
\(\frac{1}{18}\)
- (b)
\(\frac{1}{5}\)
- (c)
\(\frac{4}{5}\)
- (d)
\(\frac{17}{18}\)
If P(A) = 0.59, P(B) = 0.30 and P(A\(\cap\)B) = 0.21, then P(A'\(\cap\)B') is
- (a)
0.11
- (b)
0.38
- (c)
0.32
- (d)
None of these
A pair of dice is thrown thrice. The probability of throwing doublets at least once is
- (a)
\(\frac{1}{36}\)
- (b)
\(\frac{25}{216}\)
- (c)
\(\frac{125}{216}\)
- (d)
\(\frac{91}{216}\)
Statement-I: The event E of a sample space 5 has occurred, if the outcome \(\omega \) of the experiment is such that \(\omega \epsilon \)E.
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement -1.
- (b)
If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement -1.
- (c)
If Statement -I is true but Statement-II is false.
- (d)
If Statement-I is false and Statement-II is true.
In a non-leap year, the probability of having Tuesdays or 53 Wednesdays is
- (a)
\(\frac{1}{7}\)
- (b)
\(\frac{2}{7}\)
- (c)
\(\frac{3}{7}\)
- (d)
None of these
Three numbers are chosen from 1 to 20. Find the probability that they are not consecutive.
- (a)
\(\frac{186}{190}\)
- (b)
\(\frac{187}{190}\)
- (c)
\(\frac{188}{190}\)
- (d)
\(\frac{18}{^{20}C_{3}}\)
Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3 and 5. The probability of such a number divisible by 5 is
- (a)
\(\frac{1}{4}\)
- (b)
\(\frac{4}{5}\)
- (c)
\(\frac{1}{30}\)
- (d)
\(\frac{5}{9}\)