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Statistics and Probability

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Q 1. Two fair dice are tossed. Let {tex} x {/tex} be the event that the first die shows an even number and {tex} y {/tex} be the event that the second die shows an odd number. The two events {tex} x {/tex} and {tex} y {/tex} are:

Mutually exclusive

Independent and mutually exclusive

Dependent

None of these

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Q 2. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals

{tex} 1 / 2 {/tex}

{tex} 1 / 5 {/tex}

{tex} 1 / 10 {/tex}

{tex} 1 / 20 {/tex}

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Q 3. A six faced fair dice is thrown until 1 comes, then the probability that 1 comes in even no. of trials is

{tex} 5 / 11 {/tex}

{tex} 5 / 6 {/tex}

{tex} 6 / 11 {/tex}

{tex} 1 / 6 {/tex}

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Q 4. An experiment has 10 equally likely outcomes. Let {tex} A {/tex} and {tex} B {/tex} be non-empty events of the experiment. If {tex} A {/tex} consists of 4 outcomes, the number of outcomes that {tex} B {/tex} must have so that {tex} A {/tex} and {tex} B {/tex} are independent, is

2, 4 or 8

3, 6 or 9

4 or 8

5 or 10

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Q 5. If the frequencies of first four numbers out of {tex} 1,2,4,6,8 {/tex} are {tex} 2 , {/tex} {tex} 3,3,2 , {/tex} respectively, then the frequency of {tex} 8 , {/tex} if their {tex} A M {/tex} is {tex} 5 , {/tex} is

4

5

6

None of these

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Q 6. In a family, there are {tex}8{/tex} men, {tex}7{/tex} women and {tex}5{/tex} children whose mean ages separately are respectively {tex} 24,20 {/tex} and {tex}6{/tex} years. The mean age of the family is

17.1 years

18.1 years

19.1 years

None of these

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Q 7. The arithmetic mean of first {tex} n {/tex} odd natural numbers is

{tex} n {/tex}

{tex} \frac { n + 1 } { 2 } {/tex}

{tex} n - 1 {/tex}

None of these

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Q 8. The weighed mean of first {tex} n {/tex} natural numbers whose weights are equal to the squares of corresponding numbers is

{tex} \frac { n + 1 } { 2 } {/tex}

{tex} \frac { 3 n ( n + 1 ) } { 2 ( 2 n + 1 ) } {/tex}

{tex} \frac { ( n + 1 ) ( 2 n + 1 ) } { 6 } {/tex}

{tex} \frac { n ( n + 1 ) } { 2 } {/tex}

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Q 9. In any discrete series (when all values are same), the relationship between {tex}\mathrm{MD}{/tex} about mean and {tex}\mathrm{SD}{/tex} is

{tex} \mathrm { MD } = \mathrm { SD } {/tex}

{tex} \mathrm { MD } \geq \mathrm { SD } {/tex}

{tex} \mathrm { MD } < \mathrm { SD } {/tex}

{tex} \mathrm { MD } \leq \mathrm { SD } {/tex}

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Q 10. The mean deviation of the numbers {tex} 3,4,5,6,7 {/tex} is

0

1.2

5

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