SaiBook.us Statistics

Example

Title: Conditional probability

Grade: 9-a Lesson: S3-L6

Explanation: The best way to understand statistics is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?

Step 1a

Assumption of probability

Explanation:

Event A : First die is 5

⇒ \$P(A) = 1/6\$

Event B : Total of two dice is greater than 9

Possible outcomes for A and B:{(5,5),(5,6)}

⇒ \$P(A ∩ B) = 2/36\$

⇒ \$P(A ∩ B) = 1/18 \$

Step 1b

Finding the probability

Explanation:

P(B/A) = \$(P(A ∩ B))/( P(A))\$

where P(A) > 0

P(B/A) = \$(1/18)/(1/6)\$

P(B/A) = \$(1/18) × (6/1)\$

P(B/A) = \$1/3\$