Probability (Easy Level) - CAT MCQ

We know that the dice has only numbers 5,6 more than 4.
5 or 6 out of a sample space of 1,2,3,4,5 or 6
We also know the probability of having one number is 1/6.
Hence is P (5) or P (6) = 1/6  + 1/6  = 2/6=1/3 

Event definition: First is blue and second is blue = 7/12 X 6/11 = 7/22.

From the figure it is evident that 80 students passed at least 1 exam. Thus, 20 failed both and the required probability is 20/100 = 1/5.

With a six on the first dice, there are 6 possibilities of outcomes that can appear on the other dice (viz. 6 & 1, 6 & 2, 6 & 3, 6 & 4, 6 &5 and 6&6).At the same time with 6 on the second dice there are 5 more possibilities for outcomes on the first dice: (1 & 6, 2 & 6, 3 & 6, 4 & 6, 5 & 6)
Also, the total outcomes are 36. Hence, the required probability is 11/36.
 

Odds against an event = p(E’)/p(E)
In this case, the event is: All black, i.e., First is black and second is black and third is black.
P(E) = 5/9 X 4/8 X 3/7 = 60/504 = 5/42.
Odds against the event = 37/5.

Event definition is: 15 or 16 or 17 or 18.
15 can be got as: 
5 and 5 and 5 (one way)            
Or
6 and 5 and 4 (Six ways)        
Or 6 and 6 and 3 (3 ways)        
Total of 10 ways. 16can be got as: 6 and 6 and 4 (3ways)
Or 6 and 5 and 5 (3ways) = Total 6 ways.
17 has 3 ways and 18 has 1 way of appearing. Thus, the required probability is: (10 + 6 + 3 + 1)/216 = 20/216 = 5/54. 

Positive outcomes = 2 (187 or 215) Total outcomes = 9 X 8 X 7
Required probability = 2/504

Sum less than 10 is the non event for the case sum is 10 or 11 or 12. There are 3 ways of getting 10, 2 ways of getting 11 and 1 way of getting a sum of 12 in the throw of two dice. 
Thus, the required probability would be 1 – 6/36 = 5/6.

Probability of winning X Reward of winning = (10/5000) X 1 crore = (1 crore/500) = 20000.

Once a black ball is selected, the probability of black is going to get affected as the number of black balls & total balls decrease by a number of 1 for each removal of blackball.
Black and Black and Black = 4/9 X 3/8 X 2/7 = 24/504 = 1/21.

Positive Outcomes are: 5, 7, 10, 14, 15 or 20 - which are 6 in number out of 20 balls From the equation of probability, we get 6/20 = 3/10.
 

The required probability would be given by:
All are Red OR All are white OR All are Blue
= (6/18) X(5/17) X(4/16) + (4/18) X(3/17) X(2/16) + (8/18) X(7/17) X(6/16) 
= 480/(18 X17 X16) = 5/51