Math Question and Answer

Introduction to Online Study about Calculating Probability :

The Probability calculator online includes some axioms on the topic and some problems .Probability is defined as a measure of uncertainty of various phenomenon. While throwing a die, we would have observed that the top face of the die could be 1 or 2 or 3or 4 or 5 or 6. The set which has all the possible outcomes while performing an experiment is called as Sample space. While throwing a die, the sample space = { 1, 2, 3, 4, 5 6}. To obtain the probability of an event, we find the ration of the number of outcomes favorable to an event, to the total number of equally likely outcomes. So, probability of getting an even number while throwing a die is 3/6 since the even numbers among the six numbers are 2, 4 and 6.(i.e., 3 in number)

Axioms Involved in Calculating Probability :

Axioms in probability:
P(A U A') = P(S)
P(A) + P(A') = 1
P(A') = 1 - P(A)

Calculating Probability of an Event :

• One card is drawn from a well shuffled pack of 52 cards. If each outcome is equally likely, calculate the probability that the card will be 1. a diamond 2. not an ace 3. a black card 4. not a diamond 5. not a black card.
• Need help Probability calculator

Solution:
A well shuffled pack has 52 cards. So, n(S) = 52
1. Let A be the event of getting a diamond card. Number of diamond cards in the 52 cards are 13.
So, Probability of getting a diamond card = 13/ 52 = 1/4.
2. Let B be the event of getting not an ace card. There are 4 aces in 52 cards. Number of cards that are not ace = 52 - 4 = 48 cards
So, Probability of getting not an ace card = 48/52 = 12/13.
3. Let C be the event of getting a black card. Number of black cards in 52 cards are 26.
So, Probability of getting a black card = 26/52 = 1/2
4. let D be the event of getting a non diamond card. There are 13 diamond cards in 52 cards. Number of cards that are not a diamond is 52 - 13 = 39 cards.
So Start Growing up with Mathematics, Probability of getting a non diamond card = 39/52 = 3/4
5. Let E be the event of getting not a black card. E is the complement event of C.
So, P(not C) = P(C') = 1 - P(C) = 1- 1/2 = 1/2