Probability Quiz-1

Total balls = 23+12+15 = 50

Non red balls = 12+15 = 27

Required Probability =  \frac{27}{50}

P(A ∪ B) = P(A) + P(B) - P(A∩B)

=> P(A ∪ B) = 0.37 + 0.32 - 0.11 = 0.58

The probability of telling truth by Raj = 0.26

The probability of telling lie by Raj = 1 -0.26 = 0.74

The probability of telling truth by Aman = 0.20

The probability of telling lie by Raj = 1 - 0.20 = 0.80

 

They will contradict each other when Raj speaks the truth and Aman speak a lie and vice versa

Required probability = 0.26 x 0.80 + 0.74 x 0.20 = 0.356

multiple of 3 from 41 to 70 = {42, 45, 48, 51, 54, 57, 60, 63, 66, 69} is 10

Required Probability =  \frac{10}{30} = \frac{1}{3}

2014 is non-leap year so 365 days

No of wednesday = 52+1 = 53

Required Probability =  \frac{53}{365}

Total Possible combinations = 4 x 4 x 4 x 4 = 256

Password has to divisible by 5 for that Possible combinations = 4 x 4 x 4 x 1 = 64

Required Probability =  \frac{64}{256} = \frac{1}{4}

Total number of students  = 25+15 = 40

Total number of selecting 2 students = ^{40}\textrm{C}_{2} = 780

No of ways of selecting 1 girl and 1 boy =  ^{25}\textrm{C}_{1} \times ^{15}\textrm{C}_{1} = 375

Required Probability =  \frac{375}{780} = \frac{75}{156}

Two digit total possible numbers using digits 3, 9, 1, and 8 = 4 x 4 = 16

For a number to be divisible by 2 here unit digits are only 8 possible

Then the total number of possible combinations for divisible by 2 = 4 x 1 = 4

Required Probability =  \frac{4}{16} = \frac{1}{4}

Probability that all test cases passed = 0.22 x 0.2 x 0.1 = 0.0044

The probability of selection of  Pulikit is 0.3 

The probability of not selection of Pulikit is 0.7

 

The probability of selection of  Aman is 0.4

The probability of not selection of  Pulikit is 0.6

 

The probability that any one of them is selected = 0.3 x 0.6 + 0.7 x 0.4 = 0.46