# Solving Probability

SOLVING PROBABILITY

Classical Definition of PROBABILITY

If an experiment can result in a certain number of possible outcomes N, then the probability of the occurrence of an event A is:

number of occurrences of A

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Total number of possible outcomes

Example (1) :

A fair coin is tossed three times. Find the probability of getting at least . two heads.

Solution :

Let A = be the event of getting at least two heads

Let S = Sample Space which refers to the total number of possible outcomes

S = ( HHH, HHT, HTH, THH, HTT,THT,TTH,TTT ) = 8

A = ( HHT, HTH, THH, HHH ) = 4

P(A) = 4/8 = 1/2

The probability of getting at least two heads when a coin is tossed three times

Is ½.

Example ( 2 ) :

To form a committee, four people are to be selected from a group of five

doctors and five lawyers. Find the probability of including two doctors in the

committee.

First find the Sample Space which is total number of possible committees

consisting of four members selected from ten members.

Sample Space = 10 C 4 = 10 !/ (10 - 4)! 4! = 210

Next find the number of possible committees formed consisting of two doctors.

Let this be n.

n = 5 C 2 * 5 C 2 = 5! / 3! 2! * 5!/3! 2!

= 10 * 10 = 100

P(A) = n / Sample Space = 100 / 210 = 10/ 21

The probability of including two doctors in the committee is 10/21.

## Comments

I always have problems with Probability, :) but is really useful.

Cristina, can you give us more layman applications? For example, I reduce the probability of getting hurt in accidents by following most traffic rules, and even making some of my own for myself. No use to fatalists, of course. ;)

i like ur presentation but can you give me examples for the success probability factor??

from a bag containing 6 white marbles and 8 blue marbles, 4 marbles are chosen at random. Find the probability that 2 white and 2 blue marbles are chosen.

A company has just promoted 8 of its employees. Out of their total staff, 60% are women.

What would be the probability that 6 or more of the employees promoted are women, if promotions happened by chance??

can anyone help me with this question

A cube that has one of the letters A,B,C,D,E and F on each face is thrown. What is the probability of the F landing face-down?

i think it will be 1/6 and tell me if i ame right im only in 7 grade ok bye bye ^_^

becase that are only 6 answers so f is 1 of them so it has 2 b e 1 out of 6 / ps i ment to say im in 7 grade ok thanks bye bye ^_^lol lol lol

i think am now good to handle a probability exam thanks to you people

A coin is tossed 6 times. Find the probability of getting at least two heads?

6C2 (1/2)2 (1/2)4 + 6C3 (1/2)3 (1/2)3 + 6C4 (1/2)4 (1/2)2 + 6C5 (1/2)5 (1/2)1 6C6 (1/2)6 (1/2)0

= 15/64 + 20/64 + 15/64 + 6/64 + 1/64

=57/64

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