SaiBook.us Statistics

Lesson Example Discussion Quiz: Class Homework

Example

Title: Addition theorem for mutually exclusive events

Grade: 9-a Lesson: S3-L5

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

Examples:

A herd contains 30 cows numbered from 1 to 30. One cow is selected at random. Find the probability that number of the selected cow is a multiple of 5 or 8.

Step 1a

Assumption of probability

Explanation:

Numbers being a multiple of 5 within 30

⇒ Favourable cases or Sample space(5):{5,10,15,20,25,30}

Event A : Event of number being a multiple of 5 within 30

⇒ \$P(A) = 6/30\$

Numbers being a multiple of 8 within 30

⇒ Favourable cases or Sample space(8):{8,16,24}

Event B : Event of number being a multiple of 8 within 30

⇒ \$P(B) = 3/30\$

Step 1b

Finding the probability

Explanation:

P (A ∪ B) = P(A) + P(B)

P (A ∪ B) = \$(6/30) + (3/30)\$

P (A ∩ B) = \$(6+3)/30\$

P (A ∩ B) = \$9/30\$

P (A ∩ B) = \$3/10\$

Probability that number of the selected cow is a multiple of 5 or 8 = \$3/10\$