Expected Value Sum

Introduction to Expected value:

The expected value is nothing but the problem that has many possibilities of occurring  the expected value for the particular problem. Computing of expected value can be clearly explaining you through the probability topic in math, hence the probability has many possibilities of solutions. Thus, the dice and coins play a important role to help you better in expected value.

I like to share this Expected Value of Uniform Distribution with you all through my article.


Expected value Sum - Example Problems:

Problem 1: A perfect cubic die is thrown. Find the probability that

i)an even numbers comes up.

ii)a perfect square comes up.

Solution:

Since a die can result in six outcomes, n(S) =6. All these outcomes are equally likely.

Let A be the event, that an even number comes up.

Then        A = {2, 4, 6}

P(A) = n(A)/n(S)

= 3/6

= 1/2


Let B be the event that a perfect square comes up. Since the only perfect squares in S are 1 and 4,

Therefore B = {1, 4}.

Therefore n(B) = 2,

P(B) = n(B) / n(S)

= 2 /6

= 1/3.

Problem 2:

A box contains 7 red, 3 White and 2 black balls. When a ball is picked up at random from the box find the probability that,

i)it is Red.

ii)it is not Red.

Solution:

The total number of balls in the box is 7 + 3 + 2 = 12

Hence, n(S) = 12.

i)Let A denote the event that the ball drawn is Red.

Since there are 7 Red balls in the box, therefore, n(A) = 7

Therefore  P(A) = n(A) /n(S)

= 7 /12

ii)P (the ball is not Red) = P(A’)

= 1 – P(A)

= 1 – 7 /12

= 5 / 12

We also proceed directly as follows:

When the ball is not Red, it is from the remaining color that’s from the 3 white balls or 2 black balls.

Therefore n(A’) = 3 + 2 = 5.

Hence, P(A’) = n(A’) / n(S)

= 5 / 12.


Expected value Sum - Practice Problems:


Practice Problem: 1

It is found that, when A and B play a game of chess, the odds in favour of A winning the game are 3:5. Find the probability of
i) A winning the game.

ii) A not winning the game.

Answer :

i)     3/8
ii)    5/8
2. An unbiased coin is tossed. Find the probability that

i) A tail turns up,

ii) Both Head and Tail turn up,

iii) Neither Head nor Tail turns up.

Answer:

i)        1/2
ii)       1/2
iii)       0