Probability

The probability is number of possible outcomes is divided in to the total number of possibles. This is probability. The probability contains two types of distributions these are the continuous probability and the discrete probability. The continuous probability is contains Binomial distribution, normal distribution, continuous uniform distribution, and Gamma distribution. The general formation of the probability is

Probability P (A) = "Number of possible outcomes n (a)" / ("Total Number of outcomes n(s)")

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Examples of Probabilities:

Probability - Example 1:

Roll a dice; find the probability of exactly 2.

Solution:

Total Number of possible = n (a) = {1, 2, 3, 4, 5, 6}

n (s) = 6

The number of outcomes n (a) ={2}

n (a) = 1

The probability of getting value = 1/6 .

Probability - Example 2:

Tossing three coins and finds the probability of two tails and so one head. The possible outcomes are:

Solution:

Step 1:

n (s) = {TTT, TTH, THT, THH, HTT, HTH, HHT, HHH}=8

Step 2:

There are 3 tosses with only one head:

n (a) = {TTH, THT, HTT}=3

Step 3:

Formula:

P (A) = (n(a))/(n(s))

Answer:

P (A) = 3/8 .

Probability - Example 3:

Three cabin van colors red and green. Cabin 1 has 10 vans of red and 10 vans of green, cabin 2 has 7 vans red and 3 green vans and cabin 3 contains 6 red vans and 4 green vans. The respective probabilities of choosing a cabin are 1/4, 1/6, 1/8. What is the probability that the van chosen is green?

Solution

We begin by defining the following sets. Let,

G = the ball chosen is green.
C1 = Cabin 1 is selected
C2 = Cabin 2 is selected
C3 = Cabin 3 is selected

Then P (G|C1) = 10/20 , P(G|C2) = 3/10 and P(G|C3) = 4/10 .

P(G) = ((10/20)xx(1/4)) + ((3/10)xx(1/6))+((4/10)xx(1/8)) = 9/(40)

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Probability - Example 4:

The odds in possible of occurrence of an event 8: 17. Find the probability of the occurrences of this event

Solution:

Number of possible outcomes = 8.

Number of non-possible outcomes = 17.

Total number of outcomes = (8+17) = 25.

P (E) = (Number of the favorable outcomes)/(Number of the unfavorable outcomes)

= 8 / 25.