Learn Probability Expected Value

The total number of events of a sample space is n and the total number of possiblities of event A is m.then the probability of event A is given as P(A) = m/n

If a variable x can take any of values (x1, x2, …..xn) with the corresponding probabilities (P1, P2,....Pn) then

expected value of x is written as E(x) = P1X1+ P2X2+......+PnXn. E(x) is called expected value in probability. The expected value of x is also known as exception of x.

Probability and expected values are used in statistics, economics and finance.Expected value is the avaerage of all possible values and it is very useful for making decisions in economics and finance.The games of gambling can be won by finding the expected values.Example the roulette is a big spinning wheel with a silver ball, the wheel is rotated and the ball is dropped on it.The wheel has numbers 0 to 36 and a 00 - total possiblities are 38.

I like to share this Tree Diagram Probability with you all through my article.

Examples problems on learning probability of expected value:

The probability of a specific problem being solved independent by A and B are 1/2 and 1/3 respectively. If two equations  are on solving the problem independently, find the probability that

(i) Problem is solved.

(ii) Exactly one of them solves the problem.

Sol :

Step 1:   Let E1 = event that A solves the problem,

and E2 = event that B solves the problem.

Then ,P(E1) = 1/2  and P(E2) = 1/3

Step 2:P(E1') = (1 - 1/2 )

= 1/2

Step 3:   ==>P(E2') = (1 – 1/3 )

= 2/3 .

Clearly, E1 and E2 are independent events.

Step 4:  Therefore P(E1 nn  E2) = P(E1) x P(E2)

= (1/2 x 1/3 )

= 1/6 .

Step 4:     (i)P(problem is solved)

= P(at least one of A and B solves the problem)

= P(E1 or E2) = P(E1 uu  E2)

=P(E1) + P(E2) – P(E1nn E2)

= (1/2 + 1/3 – 1/6 )

= 4/6

= 3/2.

Step 5:(ii)P(exactly one of them solves the problem)

=P(E1 and not E2) or (E2 and not E1)

=P(E1 and not E2) + (E2 and not E1)

=P(E1nn   E2) + P(E2nn  E1)

=P(E1) x P(E2) + P(E2) x P(E1)

=(1/2 x 1/3 ) + (1/3 x 1/2 )

=(1/3 + 1/6 )

= 3/6

=1/2.

My forthcoming post is on system of linear equations word problems and cbse 9th class sample papers 2011 will give you more understanding about Algebra.

Practice problems on learning probability:

The odds against a man who is 45 years old, living till he is 70 are 7 : 5, and the odds against his wife who is now 36, living till she is 61 are 5 : 3. Find the probability that

(i) The couple will be alive 25 years hence

(ii) At least one of them will be alive 25 years hence.

(Ans: 61/96 ).