Category: Challenging questions

Challenging Probability problem 5

An unbiased die is thrown 6 times. Calculate the probabilities that the six scores obtained will

i) be 1, 2,3, 4, 5,6 in some order

ii) have a product which is an even number

iii) consists of exactly two 6’s and four odd numbers

Solution

dice prob

iii Alternative solution

6C2: 6 slots choose 2 slots to insert the two 6s. Remaining 4 slots automatically will be for the four odd numbers.
3^4: Each odd number has 3 choices. for 4 odd numbers will be 3^4
Probability = (6C2 x 3^4) / 6^6 = 5/192

 

Calculating Mean and Variance of coded data

coded-data

Venn diagram, Inclusion and Exclusion Principle

Venn diagram, Inclusion and exclusion principle can be useful in solving permutations, combinations and probability problems.

It is especially useful in solving combinations where the cases are not mutually exclusive and hence addition principle cannot be applied.

Example 1

venn diagram pnc

venn diagram p2

Challenging Normal Distribution problem 2

normal

See Square root of x squared

Finding suitable replacement to solve new inequalities

ineq1

ineq2

ineq3