Calculate Probability

Probability is a calculation of uncertainty of actions in a random experiment. Assumes that if a process a large number of times  'n' and if event 'A'  occurs 'x'  of these times then probability of event A meet on  x / n   as n becomes big.
No. of possible sets(x)
The probability of event A = ------------------------------------
Total no. of sets (n)

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Problems based on Probability:

1) In a car shop there are 8 blue cars, 5 white cars, and 8 black cars are landed. calculate the probability of choosing Blue cars?

Solution:

Total number of cars = 21

Number of Blue cars = 8
Number of Blue cars
The probability of choosing Blue car = ----------------------------------
Total number of cars

= 8/21.

2) In an Ice-cream parlor there are 6 vanillas, 8 chocobars and 5 strawberries are available. Calculate the probability to choose ice-cream that is not vanilla.

Solution:

Total number of ice-creams = 19

Number of ice-cream that not vanilla = total number of ice-cream – number of vanillas

= 19 – 6

= 13
Number of ice-cream that not vanilla
Probability of vanilla not chosen  =  --------------------------------------------------
Total number of ice-creams

= 13/19.

Problem based on priority:

At a toy shop there are 150 Toys, 50 are Barbie, 30 are Dora and the remainder are Jerry. Every Toy is equally likely to purchase, Calculate the probability:

a) Dora purchased first.

b) Jerry purchased first.

c) Barbie purchased second if either a Jerry or Dora had purchased first.

Solution:

a) Let S be sample space and A be event of Jerry purchased first.

n(S) = 150

n(A) = 30

Probability of Dora purchased first:

P(A) = 30/150 = 1/5

b) Let B be event of Jerry purchased first.

n(B) = 150 – 50 – 30 = 70

Probability of Jerry purchased first:

P(B) = 70/150 = 7/15

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c) If either a Dora or Jerry had purchased first, then there are 149 Toys remaining, 50 of which are Barbie. Let T be the sample space and C be the event of a Barbie purchased.

n(T) = 149

n(C) = 50

Probability of Barbie purchased:

P(C) = 50/149.