The Manager of a company accepts only one employees leave request for a particular day. If five employees namely Roshan, Mahesh, Sripad, Laxmipriya and Shreyan applied for the leave on the occasion of Diwali. What is the probability that Laxmi priya?s leave request will be approved ?

Correct Answer: 3/10

Explanation:

Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20
Let E = event of getting a multiple of 4 or 15
=multiples od 4 are {4, 8, 12, 16, 20}
And multiples of 15 means multiples of 3 and 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}.
= the common multiple is only (15).
=> E = n(E)= 6
Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10.

Correct Answer: 3/4

Explanation:

Let S be the sample space.
Here n(S)= 2 3 = 8
Let E be the event of getting atmost two heads. Then,
n(E) = {(H,T,T), (T,H,T), (T,T,H), (H,H,T), (T,H,H), (H,T,H)}
Required probability = n(E)/n(S) = 6/8 = 3/4.

Correct Answer: 9/13

Explanation:

There are 13 spade and 3 more jack Probability of getting spade or a jack: =13+352=1652=413   So probability of getting neither spade nor a jack: =1?413 = 9/13

Correct Answer: 1/221

Explanation:

 Let S be the sample space

 

Then, n(S) =  52 C 2= 1326.

 

Let E = event of getting 2 kings out of 4.

 

n(E)  =  52 * 51 2 * 1= 6.

  4 C 2

=> 4 * 3 2 * 1

P ( E ) = n ( E ) n ( S ) = 6 1326 = 1 221

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

Correct Answer: 2/3

Explanation:

S = { 1, 2, 3, 4, .....18 } 

=> n(S) = 18

 

E1 = {2, 4, 6, 8, 10, 12, 14, 16, 18}

=> n(E1) = 9

 

E2 = {3, 6, 9, 12, 15, 18 }

=> n(E2) = 6

 

  E 3 = E 1 ? E 2 = { 6 , 12 , 18 } 

=> n(E3) = 3

 

? E = E 1 ? E 2 = E 1 + E 2 - E 3 

=> n(E) = 9 + 6 - 3 =12

 where E = { 2, 3, 4, 6, 8, 9, 10, 12, 12, 14, 15, 16, 18 }

 

? P ( E ) = n ( E ) n ( S ) = 12 18 = 2 3

Correct Answer: 55/221

Explanation:

n(S) =  C 2 52 = 1326

 

 Let  A = event of getting both red cards

 

and B = event of getting both queens

 

then  A ? B = event of getting two red queens

 

n(A) =  C 2 26 = 325,   n(B) =  C 2 4 = 6

 

  n ( A ? B ) = C 2 2 = 1

 

  ? P A = 325 1326 , P B = 6 1326

 

  P A ? B = 1 1326

 

?P ( both red or both queens) =  P A ? B

 

=  P A + P B - P A ? B = 325 1326 + 1 221 - 1 1326= 55 221

Correct Answer: 4/7

Explanation:

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) = 8 /14=4/7.

Correct Answer: p/(p+q)

Explanation:

Total number of cases=p+q

Favourable cases=p

Probability of that event is=p/(p+q)

Correct Answer: 1/5