# Aptitude Chapter-9

The competitive bank exams probability in this chapter we are discussing Probability, Seating Arrangements. We will see how to solve through equations and through shortcut methods.

Probability: Probability = number of favorable changes / total number of chances.

### competitive bank exams probability

Suppose if you toss a coin

Total number of chances ={ H, T } = 2

Probability = ½

The problems on coin, dice, cards, and boxes.

Coin:

If you toss one coin { H, T } = 2

Two coins { HH TT HT TH } = 4

Three coins = { HHH  TTT  HTH  THT  TTH  HHT HTT THH } = 8

So the chances are 2^n

Example :

Three unbiased coins are tossed what is the probability of getting at most two heads ?

1. a) ½ b) 1/8    c) ¾    d) 8/7

Three coins are tossed so total number of chances 2^3=8

We require at most two heads that means maximum two heads. The favorable chances are :

{ TTT, HTT, TTH, THT, HHT, HTH, TTH } = 7

So Probability = 7/8

Dice:

Dice has 6 faces so if we throw a dice possible chances = 6.

Two dice = 36  = 6^2

Three dice =216  = 6^3

So total number of chances  =6^n

Example:

In a simultaneous throw of two dice, what is the probability of getting doublet ?

1. a) 1/6 b) 5/6   c) 6/5  d) 5/36

Here two dice so total number of chances  6^2 = 36

Doublet means the same number

i.e (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) = 6

The favorable chances = 6

So probability = 6/36 =1/6

Cards:

Total 52 cards

red  =26

black =26

26 red    = 13 Hearts + 13 Diamonds

26 black = 13 spades + 13 clubs

In every 13 = A+K+Q+J+2…..+10 number cards

There are 16 face cards

#### Seating arrangements:

In seating arrangements, we have to find out person’s position and a total number of persons in the arrangement.