### Mathematics - Probability

#### Question - 1

The probability that a leap year has 53 sundays

• A $\cfrac { 1 }{ 7 }$
• B $\cfrac { 2 }{ 7 }$
• C $\cfrac { 3 }{ 7 }$
• D $\cfrac { 4 }{ 7 }$

#### Question - 2

If A and B are two events such that $P(A\cup B)=0.72$, $P(A\cap B)=0.18$, and  $P(\overline { B) } =0.9$, then P(A) equals

• A 0.6
• B 0.7
• C 0.8
• D 0.9

#### Question - 3

Thr probabilities of occurance of two events A and B are 0.25 and 0.5 respectively. The probability of their simultaneous occuring is 0.14; then the probability that neither of these occurs, is

• A 0.21
• B 0.27
• C 0.35
• D 0.39

#### Question - 4

The probability of a five-digit number formed by the digits 0, 1, 2, 3, 4 which is divisible by 4 is

• A $\cfrac { 5 }{ 16 }$
• B $\cfrac { 3 }{ 8 }$
• C $\cfrac { 7 }{ 16 }$
• D $\cfrac { 9 }{ 16 }$

#### Question - 5

The probability that a teacher will give an unannounced test during any class is $\cfrac { 1 }{ 5 }$. If a student is absent twice, the probability that he misses at least one test, is

• A $\cfrac { 16}{ 25 }$
• B $\cfrac { 9 }{ 25 }$
• C $\cfrac { 1 }{ 25 }$
• D NONE OF THESE

#### Question - 6

Out of (2n+1) tickets consecutively numbered, three are drawn at random. The probability that numbers are in A.P., is

• A $\cfrac { 1 }{ 4{ n }^{ 2 }-1 }$
• B $\cfrac { 2 }{ 4{ n }^{ 2 }-1 }$
• C $\cfrac { 3n }{ 4{ n }^{ 2 }-1 }$
• D $\cfrac { 4n }{ 4{ n }^{ 2 }-1 }$

#### Question - 7

The probabilities of A, B and C solving a problem are $\cfrac { 1 }{ 2 } ,\cfrac { 1 }{ 3 }$ and $\cfrac { 1 }{ 4 }$ respectively. They work independently. The probability of the problem being solved, is

• A $\cfrac { 1 }{ 2 }$
• B $\cfrac { 3 }{ 4 }$
• C $\cfrac { 1 }{ 24 }$
• D NONE OF THESE

#### Question - 8

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 $\cfrac { 1 }{ 8 }$

#### Question - 9

Out of n persons sitting in a row, the probability that two of the selected persons do not sit side by side, is

• A $\cfrac { 2 }{ n }$
• B $1-\cfrac { 1 }{ n }$
• C $1-\cfrac { 2 }{ n }$
• D None of these

#### Question - 10

Ten persons are sitting on a round table. The probability of three particular persons, sitting together, is

• A $\cfrac { 5 }{ 12 }$
• B $\cfrac { 7 }{ 12 }$
• C $\cfrac { 11 }{ 12 }$
• D $\cfrac { 1 }{ 12 }$