OR rules for Mutually exclusive events

Independent events

Conditional Probability

Binomial Situation

The “at least” scenario

Formulae

1. Permutation & Combination

   Permutation	Combination
   Pick & put into order	Just pick, order doesn’t matter
   n! / (n-k)!	n! / [(n-k)! * k!]
   Out of A,B, C, D, E, given the task of arranging 3 objects will be 5!/2! since here A-B-C, B-A-C, A-C-B etc. are counted as different cases	Out of A,B, C, D, E, given the task of picking 3 objects will be 5!/(2!*3!) since here A-B-C, B-A-C, A-C-B etc. are counted as the same case

2. OR Rules

   <aside> ⚡ $P(A or B) = P(A) + P(B) - P(A and B)$

   </aside>

   For mutually exclusive events, $P(AandB) = 0$

3. For independent events

   <aside> ⚡ $P(AandB) = P(A)*P(B)$

   </aside>

4. Conditional Probability → non-independent events (mostly deals with the “without replacement” cases)

   <aside> ⚡ $P(AandB) = P(A)*P(B|A)$ $P(AandB) = P(B)*P(A|B)$

   </aside>

5. Binomial → probability of r successes in n independent trials

   <aside> ⚡ $P = C^n_rp^r[(1-p)^{n-r}]$

   </aside>

6. “Atleast one”

   <aside> ⚡ $P(atleast1success) = 1 - P(nosuccess)$

   </aside>

7. The conditions of “mutually exclusive” and “independent” are not common with people. More common with inanimate objects with dice, coins, cards, etc.

8. Selection processes that are “without replacement” are NEVER independent.

9. Overlap strategy for estimating answer range

   

10. When to use which technique

    1. Use formal algebraic rules IF

       

    2. Use listing IF

       

    3. Use counting technique if

       

    4. Complement rule → if you see a “atleast one” scenario