TRICK Probability

TRICK

Probability = Occurrence of event/Total possible events
Simple probability problemSimplest questions asked in bank exams are asked about deck of cards, dice and coins. There is no co-occurrence of events.
Lets take an example :-
Question -One card is drawn from a deck of 52 cards. Find the probability that it is a black queen or king.
Simple solution to this problem is 2/52 = 1/26
Venn Diagram
Question - One card is drawn from a deck of 52 cards. Each card is equally likely to be drawn. Find the probability that card drawn is either black or queen.
In this question we are going to use a simple formula
P(AB) = A ∪ B ∩ AB
Don't be confused with the formula.
In a deck of cards there are 26 black cards and 4 queens. But 2 black cards are queen. These cards are part of grey and brown circles in above diagram. As pink region is added twice, we need to deduct it once.
So the solution is 26 + 4 - 2 = 28
Probability (AB) = 28/52 = 7/13
Independent Events
In case you need to find probability of happening of two independent events we use multiplication theorem.
P(AB) = P(A) * P(B)
Lets understand this theorem with help of an example
Question -An unbiased coin is tossed twice. Find the probability of getting 1,2,3 or in the first toss and 4,5 or 6 in second attempt ?
Solution -Probability of getting 1,2,3 or 4 in first toss = 4/6 = 2/3
Probability of getting 4,5 or 6 in second toss = 3/6 = 1/2
Now both events are independent and we will use multiplication theorem
1/2 * 2/3 = 1/3