A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

Correct Answer: 1/2

Explanation:

Here, s={H,T} and E={H}
P(E) = n(E)/n(S) = 1/2

Correct Answer: 0.043

Explanation:

 Vowels are A I A I O, 

 

 C    A   S    T   I    G   A    T   I    O   N

 

(O) (E) (O) (E) (O) (E) (O) (E) (O) (E) (O)

 

So there are 5 even places in which five vowels can be arranged and in rest of 6 places 6 constants can be arranged as follows :

 

n ( E ) = 5 P 5 2 ! * 2 ! ( A , I a r e 2 t i m e s ) * 6 P 6 2 ! ( T i s 2 t i m e s ) = 21600

 

n ( S ) = 11 ! 2 ! * 2 ! * 2 ! ( A , I a r e 2 t i m e s ) = 4989600

 

21600 4989600 = 0 . 043

Correct Answer: 31 Dec

Correct Answer: 39

Explanation:

Let the average after 17th innings = x
Then average after 16th innings = (x - 3)
Therefore 16 × (x - 3) + 87 = 17x
Therefore x = 39

Correct Answer: 50 2/7 sq.cm

Correct Answer: 1/30

Correct Answer: (1/2)^11

Explanation:

Probability of occurrence of an event, 

P(E) = Number of favorable outcomes/Numeber of possible outcomes = n(E)/n(S)

? Probability of getting head in one coin = ½, 

? Probability of not getting head in one coin = 1- ½ = ½, 

Hence, 

All the 11 tosses are independent of each other.

? Required probability of getting only 2 times heads = 1 2 2 × 1 2 9 = 1 2 11

Correct Answer: 1/2

Explanation:

We know that:

When one card is drawn from a pack of 52 cards

The numbers of possible outcomes n(s) = 52

We know that there are 26 red cards in the pack of 52 cards
? The numbers of favorable outcomes n(E) = 26

Probability of occurrence of an event: P(E)=Number of favorable outcomes/Numeber of possible outcomes=n(E)/n(S)

? required probability = 26/52 = 1/2.

Correct Answer: 3 is adjacent to 5

Explanation:

If 1 is adjacent to 2, 4 and 6 then either 3 or 5 lies opposite to 1. So, the numbers 3 and 5 cannot lie opposite to each other. Hence, 3 is adjacent to 5 (necessarily).

Correct Answer: 15

Explanation:

In a usual dice, the sum of the numbers on any two opposite faces is always 7. Thus, 1 is opposite 6, 2 is opposite 5 and 3 is opposite 4.

 

Consequently, when 4, 3, 1 and 5 are the numbers on the top faces, then 3, 4, 6 and 2 respectively are the numbers on the face touching the ground. The total of these numbers = 3 + 4 + 6 + 2 = 15.