Two dice are thrown. The number of sample points in the sample space when 6 does not appear on either dice is

**A. ** 18

**B. ** 11

**C. ** 25

**D. ** 30

**Answer : ****Option C**

**Explaination / Solution: **

total no. of outcomes=62=36

The pair which shows 6 on either dice are {(6,1),(6,2),(6,3),(6,4),(6,5),(1,6),(2,6),(3,6),(4,6),(5,6),(6,6)}=11

So total number of sample points in sample space when 6 on either dice do not appear=36-11=25

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From a pack of 52 cards, the cards are drawn one by one till an ace appears. The chance that an ace does not come up in first 26 cards is

**A. ** None of these

**B. ** 23/ 27

**C. ** 109/ 153

**D. ** 46/ 153

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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If and are two independent events, then P is equal to

**A. ** P(E1)+P(E2)+P(E1+∪E2)
**B. ** P(E1)P(E2)
**C. ** None of these
**D. ** P(E1) +P (E2)
**Answer : ****Option B**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The probability that a man will live for 10 more years is and that his wife will live 10 more years is. The probability that neither will be alive in 10 years is

**A. ** 12
**B. ** 1112
**C. ** 512
**D. ** 712
**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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A coin tail on both sides is tossed twice. The probability of getting ‘a head’ is

**A. ** 1

**B. ** 3/4

**C. ** 1/2

**D. ** 0

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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If the letters of the word ‘ INDEPENDENCE ‘ are written down at random in a row , then the chance that no two E’s occur together is

**A. ** 14/ 55

**B. ** 1/ 55

**C. ** None of these

**D. ** 54/ 55

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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Coefficient of correlation between the observations ( 1, 6 ) , ( 2 , 5 ) , ( 3 , 4) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) is

**A. ** -1

**B. ** 0

**C. ** 1

**D. ** None of these

**Answer : ****Option A**

**Explaination / Solution: **

use,r(x,y)=1n∑i=1n(Xi−X¯)(Yi−Y¯)1n∑i=1n(Xi−X¯)2√1n∑i=1n(Yi−Y¯)2√

use,r(x,y)=1n∑i=1n(Xi−X¯)(Yi−Y¯)1n∑i=1n(Xi−X¯)2√1n∑i=1n(Yi−Y¯)2√

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The mean weight of a group of 10 items is 28 and that of another group of n items is 35.The mean of combined group of 10 + n items is found to be 30. The value of n is

**A. ** 4

**B. ** 2

**C. ** 10

**D. ** 12

**Answer : ****Option A**

**Explaination / Solution: **

sum of weights of 10 items =280

sum of weights of n items = 35n

so, sum of weights of ( 10 + n) items = 280 + 35n

so ,mean = (280 + 35 n) / ( 10 + n)

30(10 + n ) = 280 + 35n

solving we get, n = 4

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The mean of the first n terms of the A.P. (a + d ) + ( a + 3d ) + ( a + 5d ) +………..is

**A. ** (a+nd)/2

**B. ** a + nd

**C. ** a+n2d
**D. ** a+n2d
**Answer : ****Option B**

**Explaination / Solution: **

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ρ(X,Y) is equal to

**A. ** COV(X,Y)VAR(X)VAR(Y)
**B. ** COV(X,Y)

**C. ** cov(x,y)/sd

**D. **
**Answer : ****Option D**

**Explaination / Solution: **

=

=

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