A six-sided die with faces numbered 1 through 6 is rolled three times. What is the probability that the face with the number 6 on it will not face upward on all the three rolls?

Correct Answer: 91/190

Explanation:

Total number of elementary events = 20 C 2 ways =190

 

There are 7 white balls out of which one white can be drawn in 7 C 1 ways and one ball from remaining 13 balls can be drawn in 13 C 1 ways.

 

So,favourable events =  7 C 1 * 13 C 1

 

Therfore,required probability = ( 7 C 1 * 13 C 1)/ 20 C 2=91/90

Correct Answer: 1/2

Explanation:

Total number of elementary events = 52

 

There are 26 red cards,out of which one red card can be drawn in 26 C 1 ways =26.

 

So,required probability = 26/52 = 1/2

Correct Answer: 10/21

Explanation:

4 persons can be selected from 9 in 9 C 4 ways =126

 

Fvaourable events = 4 C 2 * 5 C 2 =60

 

So,required probability = 60/126 = 10/21

Correct Answer: 0.9375

Explanation:

Here,n = 4(children)

P(girl)= 0.5

P(of atleast one girl)= 1 - P(no girls)

                             = 1 - 0.0625 = 0.9375

Correct Answer: 2/13

Explanation:

Number of queen cards = 4

Number of ace cards = 4

 P(either a queen or ace) = 4/52 + 4/52= 8/52 = 2/13

Correct Answer: 21/46

Explanation:

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

 

Then, n(S) = Number ways of selecting 3 students out of 25

 

                =  25 C 3  = 2300.

 

         n(E)= 10 C 1 * 15 C 2 = 1050. 

 

P(E) = n(E)/n(s) = 1050/2300 = 21/46

Correct Answer: 2/3

Explanation:

Total numbers in die=6

P(multiple of 2)=1/2

P(multiple of 5)=1/6

P(multiple of 2 or 5)=2/3

Correct Answer: 1/2

Explanation:

P(heart cards)=13/52

P(diamond cards)=13/52

P(heart or diamond)=13/52+13/52=1/2

Correct Answer: 1

Explanation:

P(red cards)=26/52

P(black cards)=26/52

P(red or black cards)=26/52+26/52=1

Correct Answer: 0.75

Explanation:

P(red ball) = 5/12

P(white ball) = 4/12

P(red or white ball) = 5/12 + 4/12 = 3/4 = 0.75