In a throw of a coin, find the probability of getting a head.

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: 21/38

Explanation:

n(S) =  C 2 20 = 190 

n(E) =  C 2 15 = 105 

Therefore, P(E) = 105/190 = 21/38

Correct Answer: 5/9

Explanation:

Select a number which ocurs on two dice out of six numbers (1, 2, 3, 4, 5, 6). This can be done in  C 1 6, ways.

 

Now select two distinct number out of remaining 5 numbers which can be done in  C 2 5 ways. Thus these 4 numbers can be arranged in 4!/2! ways.

 

So, the number of ways in which two dice show the same face and the remaining two show different faces is 

  C 1 6 × C 2 5 × 4 ! 2 ! = 720

 =>  n(E) = 720

  ? P E = 720 6 4 = 5 9

Correct Answer: 1/9

Explanation:

S = { (1, 1), (1, 2), (1, 3), (1, 4),(1, 5), (1, 6), (2, 1), (2, 2),.........(6, 5), (6, 6) }

=> n(S) = 6 x 6 = 36

E = {(6, 3), (5, 4), (4, 5), (3, 6) }

=> n(E) = 4

Therefore, P(E) = 4/36 = 1/9

Correct Answer: 110/129

Explanation:

Total number of possible ways = 

9 C 5 = 9 x 8 x 7 x 6 x 5 5 x 4 x 3 x 2 x 1 = 126

Number of favorable cases = 

$$\begin{gathered} 4 C 2 x 5 C 3 + 4 C 3 x 5 C 2 + 4 C 4 x 5 C 1 \\ 4 x 3 2 x 1 x 5 x 4 x 3 3 x 2 x 1 + 4 x 3 x 2 3 x 2 x 1 x 5 x 4 2 x 1 + 1 x 5 \\ = 6 x 10 + 4 x 10 + 5 \\ = 60 + 40 + 5 \\ = 105 \end{gathered}$$

 

Therefore, required probability = 105/126 = 5/6

Correct Answer: 1/2

Explanation:

P(odd) = P (even) = 1 2 1(because there are 50 odd and 50 even numbers)

 

Sum or the three numbers can be odd only under the following 4 scenarios:

 

Odd + Odd + Odd =  1 2 * 1 2 * 1 2=  1 8

 

Odd + Even + Even =  1 2 * 1 2 * 1 2= 1 8

 

Even + Odd + Even =  1 2 * 1 2 * 1 2= 1 8

 

Even + Even + Odd =  1 2 * 1 2 * 1 2 =  1 8

 

Other combinations of odd and even will give even numbers. 

 

Adding up the 4 scenarios above:

 

=  1 8+  1 8+ 1 8+  1 8 =  4 8 =  1 2

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: 9/13

Explanation:

There are 13 spades ( including one king). Besides there are 3 more kings in remaining 3 suits

 

Thus   n(E) = 13 + 3 = 16

 

Hence  n E ¯ = 52 - 16 = 36 

  

Therefore,  P E = 36 52 = 9 13

Correct Answer: 39/100

Explanation:

P ( neither A nor B) =  P A a n d B  

 

=   P A ? B=   P A ? B=  1 - P A ? B  

 

=  1 - 61 100 = 39 100