Question 12 (i) - End-of-Chapter Exercises - Chapter 7 - The Mathematics of Maybe: Introduction to Probability

Transcript

Question 12 (i) Write the sample space and calculate the probability based on the given information. (i) Two dice are rolled. What is the probability that the sum is a prime number greater than 5? Let’s look at our Sample Space Second Die First Die Now, Prime number greater than 5 are 7, 11, 13, 17, … We need Sum which is a prime number greater than 5 So, Possible sums = 7, 11 Let’s mark Sum = 7 & Sum = 11 in our Sample Space Now, Ways to get sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) ⟶ 6 ways Ways to get sum 11: (5,6), (6,5) ⟶ 2 ways Thus, Total favorable outcomes = 8 Total possible dice outcomes = 36. Therefore, Probability = (𝐹𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠) = 8/36 = 𝟐/𝟗