How to Calculate and Solve for P(A and B) | Probability

Last Updated on March 28, 2024

The image above represents P(A and B).

To compute for P(A and B), four essential parameters are needed and these parameters are x_A, N_A, x_B and N_B.

The formula for calculating P(A and B):

P(A and B) = P(A) x P(B)

Where;

P(A) =  ^x_A ⁄ _NA
P(B) = ^x_B ⁄ _NB

Let’s solve an example;
Find the P(A and B) when x_A is 2, N_A is 4, x_B is 5 and N_B is 8.

This implies that;

x_A = 2
N_A = 4
x_B = 5
N_B = 8

P(A and B) = P(A) x P(B)
P(A and B) = ^x_A ⁄ _NA x ^x_B ⁄ _NB
So, P(A and B) = ² ⁄ ₄ x ⁵ ⁄ ₈
P(A and B) = ⁽²⁾⁽⁵⁾ ⁄ ₍₄₎₍₈₎
P(A and B) = ¹⁰ ⁄ ₃₂
Divinding the numerator and denominator by 2
P(A and B) = ⁵ ⁄ ₁₆
P(A and B) = 0.312

Therefore, the P(A and B) is 0.312.

Read more: How to Calculate and Solve for P(A or B) | Probability

How to Calculate and Solve for P(A and B) Probability Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the P(A and B).

To get the answer and workings of the P(A and B) using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Probability under Mathematics.

Now, Click on P(A and B) under Probability

The screenshot below displays the page or activity to enter your values, to get the answer for the P(A and B) according to the respective parameters which are the x_A, N_A, x_B and N_B.

Now, enter the values appropriately and accordingly for the parameters as required by the x_A is 2, N_A is 4, x_B is 5 and N_B is 8.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the P(A and B) and presents the formula, workings and steps too.