SaiBook.us Statistics

Lesson Example Discussion Quiz: Class Homework

Example

Title: Multiplication theorem for dependent Events

Grade: 9-a Lesson: S3-L8

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

Examples:

A bag contains 10 white and 5 black balls.Two balls are drawn at random one after the other without replacement.Find the probability that both balss drawn are black.

Step 1a

Assumption of probability P(A)

Explanation:

Probability of drawing a black ball in the first attempt = P(A)

P(A) = \$5/(10+5)\$

P(A) = \$5/15\$

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

Step 1b

Assumption of probability P(B/A)

Explanation:

Probability of drawing the second ball given that the first ball is black and not replaced or without replacement = P(B/A)

P(B/A) = \$4/(10+4)\$

P(B/A) = \$4/14\$

P(B/A) = \$2/7\$

Step 1c

Finding the probability

Explanation:

Events are dependent,so the probability that both balls are drawn are black = P(A ∩ B)

P(A ∩ B) = P(B/A)P(A)

P(A ∩ B) = \$(2/7) × (1/3)\$

P(A ∩ B) = \$2/21\$