Today we explore the basic concepts of Probability.
Probability is the measure of the likelihood of an "event" to occur.
For example, when we toss a fair coin, the chances of a head turning up are 1/2. When we roll a dice the chance of 2 appearing is 1/6.
Important Terms:
1. Sample Space : The collection of all results is called the sample space of the event.
For example, when a coin is tossed, the Sample space(S) is the set {Head, Tails}.
When a dice is rolled, S = {1,2,3,4,5,6}
2. Event: A subset of the S is called an event. For example, when a coin is tossed, {Head}, {Tail} are events. Note that an event set can contain multiple items. For example when 2 coins are tossed, {Head,Head} is considered an event.
3. Equally Probable Events: When 2 events have the same likelihood of occuring, they are known as Equally Probable events. For example the chance of head and tails turning up on the toss of a coin are Equally Probable events.
Probability
The Probability of an
event occurring is defined as the number of cases favorable for the
event divided by total number of events in the sample space.
If the event be called as 'A', the probability is represented as P(A)
Example: Probability that head shows up on tossing a coin
Favorable Cases : Head (1)
Sample Space: Head, Tail (2)
P(A) = Favorable Cases/Sample Space = 1/2
P(A') is used to represent the probability of event A not occurring.
Note: P(A) + P(A') = 1
If we have 2 events A,B as the overall sample space, then:
P(A) = A / (A+B) and P(B) = B / (A + B)
Independent Events and Mutually Exclusive Events
A regular confusion among students is the difference between Independent and Mutually exclusive Events.
Let A, B be 2 events. P(A and B) = P (A ∩ B ) is defined as the probability that both A and B occur together.
For 2 independent events A, B, P(A ∩ B ) = P(A) * P(B)
For Mutually Exclusive events, P(A ∩ B ) = 0
This is best understood with an example.
Consider a fair coin and a fair six-sided die. Let event A be obtaining tails, and event B be rolling a 3. Then we can safely say that events A and B are independent, because the outcome of one does not affect the outcome of the other.
Here, P(A ∩ B ) = 1/2 * 1/6 = 1/12.
Here A and B are Independent Events (Not mutually exclusive).
Consider a fair six-sided dice, where even-numbered faces are colored red, and the odd-numbered faces are colored green. Let event A be rolling a green face, and event B be rolling a 6.
P(A) = 3/6 = 1/2
P(B) = 1/6
But note that A&B cannot occur simultaneously since 6 is always going to turn up on a red face.
Here, P(A ∩ B ) =0
Here A and B are Mutually exclusive events(Not independent).
In our next post we will go deeper into complex probability theory and solve a few problems and provide video solutions for the same.
This is best understood with an example.
Consider a fair coin and a fair six-sided die. Let event A be obtaining tails, and event B be rolling a 3. Then we can safely say that events A and B are independent, because the outcome of one does not affect the outcome of the other.
Here, P(A ∩ B ) = 1/2 * 1/6 = 1/12.
Here A and B are Independent Events (Not mutually exclusive).
Consider a fair six-sided dice, where even-numbered faces are colored red, and the odd-numbered faces are colored green. Let event A be rolling a green face, and event B be rolling a 6.
P(A) = 3/6 = 1/2
P(B) = 1/6
But note that A&B cannot occur simultaneously since 6 is always going to turn up on a red face.
Here, P(A ∩ B ) =0
Here A and B are Mutually exclusive events(Not independent).
In our next post we will go deeper into complex probability theory and solve a few problems and provide video solutions for the same.
CAT website is very important site.It is really big opportunity banking development .
ReplyDeleteYou are the one who can really share new knowledge with everyone. Thanks and visit the Chinese b2b platform
ReplyDeleteIt is a particularly enticing offering for prime rollers. Big guess limits, lucrative bonuses, and flexible transaction limits are just a number of the} casino.edu.kg the reason why} it attracts heavy hitters. The non-crypto deposit methods are restricted to credit cards. If you’ve had some winnings and want to money out, the extra banking choices will be a player switch and getting a examine by courier. Bets are paid even cash, but a 5% fee is charged on successful Banker bets. The hand representing the player is given facedown to the particular person with the biggest wager on the player.
ReplyDeleteI am really happy to visit your blog.keep updates more valuable information.Thank you
ReplyDeletebankrupty attorney near me
A player switch and receiving a check by courier are the additional banking options you have if you have won and want to cash out. Bets are paid out at even money, although winning Banker bets incur a 5% commission fee. The individual who placed the largest wager on the player receives the face-down hand that represents that player, how to create Wikipedia page.
ReplyDeleteNavigate the complexities of separation before divorce with expert guidance. Discover legal insights, emotional support, and practical advice to ease the process and empower your next chapter. Explore essential resources for a smoother transition.
ReplyDeleteThe topic is indeed too technical but your writing help me to understand everything right.
ReplyDeletemotorcycle accident lawyer near me
contract dispute
Probability is a branch of mathematics that deals with the likelihood or chance of different outcomes occurring. It is used in various fields such as statistics, finance, science, and everyday decision-making. The probability of an event is denoted as P(E), and the probability formula is P(E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}. Experiments, sample space, and events are key concepts in probability. Simple events consist of a single outcome, compound events consist of two or more outcomes, and complementary events are the event that does not occur. Basic probability rules include the probability of certain events, the probability of impossible events, and the sum of probabilities criminal defense lawyer arlington va.
ReplyDelete