Suppose you roll a sevensided fair die twice What is the pro

Suppose you roll a seven-sided fair die twice. What is the probability that you rolled doubles? What is the probability that either roll is a 6 or 7? What is the probability that the sum of the two rolls is 10 or that both of the rolls are odd numbers?

Solution

Dear Student Than you for using Chegg !! Given a 7 sided dice is rolled twice a) Probability that you rolled doubles => Sample space = No of possible occurences of first dice X Number of possible occurences of second dice = 7X7 = 49 Fvourable Outcomes Dice1 1 2 3 4 5 6 7 Dice 2 1 2 3 4 5 6 7 7 Occurences Probability = favourable Outcomes / Sample Space = 7/49 = 1/7 b) Probability that either roll is a 6 or 7 Facourable Outcomes 6,1 6,2 6,3 6,4 6,5 6,6 6,7 (Considering Order, there are 13 cases, cases 6,6 being considered single time) 7,1 7,2 7,3 7,4 7,5 7,6 7,7 (Considering Order, there are 13 cases, cases 7,7 being considered single time) Total is 12 favourable outcomes since 6,7 & 7,6 considered 2 times so 13 + 13 -2 =24 Probability = 24/49 = 0.489796 c) Sum of 2 rolls is 10 or bot rolls are odd number Sum 10 3,7 4,6 5,5 (Considering Order, there are 5 cases, cases 5,5 being considered single time) 5 cases Both dice odd 1 3 5 7 1 3 5 7 No of ways for odd number on dice 1 X number of ways for odd number on second dice 4C1 X 4C1 16 Sum 10 or Both dice odd 16 + 5 -3 (3 cases 3,7 & 5,5 are odd also nd leading to sum of 10 also, so considered twice) 18 Probability = 18/49 = 0.367347