Statistic and Probability : Mathematics MCQ

Q.1. Two boys  and three girls  play a tournament. Those of the same sex have equal probabilities of winning but each boy is twice as likely to win as any girl. The probability of winning the tournament by a girl is  [MP PET 2007]

A) 2/7

B) 3/7

C) 1/7

D) None of these

Explanation-

Let probability of winning of girl be x

 Probability of winning of boy = 2 x

and x + 2x = 1  x = 

 Probability of winning of girl =  .

Q.2. Two athletes A and B participate in a race along with other athletes. If the chance of A winning the race is 1/6 and that of B winning the same race is 1/8, then the chance that neither wins the race, is 

A) 1/4

B) 7/24

C) 17/24

D) 35/48

Explanation-

Chance of winning the race=

 and chance of B winning the race=

$∴ Chance of​wins​the race== $

$$

$​Hence,​chance​that​neither​wins​the​race​= $

$<br>$

$Q.3.$A speaks truth in 60% cases and b speak truth in 70% cases. The probability that they will say the same thing while describing a single events is 

A) 0.56

B) 0.54

C) 0.38

D) 0.94

Explanation-

 

Q.4. A second order determinant is written down at random using the numbers 1,-1 as elements. The probability that the value of the determinant is non zero is 

A) 1/2

B) 3/8

C) 5/8

D) 1/3

Explanation-

n(S)==16(because each of the four places can be filled in 2 ways).The zero determinants are 

 

Q.5. If n positive integers taken at random and multiplied together, than the chance last digit of the product would be 1,3,5,7 or 9 is 

A) 

B) 

C) 

D)  

Explanation-

 

Q.6. A is a set containing 10 elements. A subset P is A is chosen at random and the set A  is reconstructed by replacing the elements of P. Another subset Q and A is now chosen at random. Then, the probability that if, P and Q have no common elements, is 

A) 

B) 

C) 

D)  

Explanation-

 

Q.7. A triangle  informed with the vertices of n sided regular polygon, Then the probability that the triangle, Have exactly one side common with the side of the polygon is 

A) 

B) 

C) 

D)  

Explanation-

Total number of ways=

Favorable ways=If side AB and take one vertex out of (n-4) vertices

 

Q.8. 5 persons A, B, C, D and E are in a queue of a shop. The probability that A and E always occur together, is

A) 

B) 

C) 

D)  

Explanation-

5 persons A, B, C, D and E can stand in a queue in 5! ways. Persons a and E can occur together in 2! ways. Considering A and E as one person, there are 4 persons who can be queued up in 4! ways. So, A and E can occur together in 4!  2! ways. So, required probability =  

Q.9. If a batsman scored 70 in one innings and remained not out at 50 in the 2 nd inning . His batting average  is...

A) 60

B) 120

C) 70

D) 85

Q.10. The best statistical  measure used for comparing two series is...

A)  mean deviation 

B) range 

C) coefficient of variation 

D) none of these