Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
Advertisement Remove all ads

Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8. - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8.

Advertisement Remove all ads

Solution

Sample space = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(S) = 36

Let A be the event of getting an even number on the first time

A = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(A) = 18

P(A) = `("n"("A"))/("n"("S")) = 18/36`

Let B be the event of getting a total of face sum 8.

B = {(2, 6) (3, 5) (4, 4) (5, 3) (6, 2)}

n(B) = 5

P(B) = `("n"("B"))/("n"("S")) = 5/36`

A ∩ B = {(2, 6) (4, 4) (6, 2)}

n(A ∩ B) = 3

P(A ∩ B) = `3/36`

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= `18/36 + 5/36 - 3/36`

= `(18 + 5 - 3)/36`

= `20/36`

= `5/9`

The required probability = `5/9`

Concept: Addition Theorem of Probability
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 10th SSLC Mathematics Answers Guide
Chapter 8 Statistics and Probability
Exercise 8.4 | Q 6 | Page 330
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×