Solve the conditional probability question

Thread starter chwala
Start date Apr 15, 2021
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Conditional Conditional probability Probability

In summary, conditional probability is the likelihood of an event occurring given that another event has already occurred. It can be calculated using the formula P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of event A occurring given that event B has occurred, P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring. Unconditional probability, also known as marginal probability, is the likelihood of an event occurring without any prior information or conditions. Conditional probability takes into account additional information or conditions when calculating the likelihood of an event occurring. It is used in a variety of fields to make predictions and decisions based on existing data

Apr 15, 2021

chwala

Gold Member

Homework Statement: see attached problem below;

Relevant Equations: conditional probability

My question is on part ##c## of the problem.
Kindly see attached question,...is the second approach correct?

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Apr 15, 2021

chwala

Gold Member

my attempt...why is the second approach wrong for question ##c##?or is it also correct?

Apr 15, 2021

chwala

Gold Member

i got a little mixed up, but that's the beauty of maths ...the correct solution is
## P(B/A^{'})##=##\frac {3}{5}##

Apr 15, 2021

chwala

Gold Member

i think its now clear...phew!

FAQ: Solve the conditional probability question

What is conditional probability?

Conditional probability is a mathematical concept that measures the likelihood of an event occurring given that another event has already occurred. It is represented as P(A|B), where A is the event we are interested in and B is the event that has already occurred.

How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of events A and B by the probability of event B. In other words, P(A|B) = P(A and B) / P(B).

What is the difference between conditional probability and regular probability?

The main difference between conditional probability and regular probability is that regular probability measures the likelihood of an event occurring without any other information, while conditional probability takes into account the occurrence of another event.

Can you provide an example of a conditional probability question?

One example of a conditional probability question is: If a deck of cards contains 52 cards, including 26 red cards and 26 black cards, what is the probability of drawing a red card given that the first card drawn was a black card? This can be represented as P(Red|Black) = 26/51.

How is conditional probability used in real life?

Conditional probability is used in various fields such as statistics, economics, and biology to make predictions and decisions based on the occurrence of certain events. For example, in medicine, conditional probability can be used to determine the likelihood of a patient having a certain disease based on their symptoms and medical history.