Question

Rolling Dice 2. A pair of dice is rolled. Here is the sample space (all of the possible outcomes) of rolling a pair of dice. First Die a) In how many different ways can we roll a 7 (as the sum of the two dice)? What is the probability of rolling a 7? 2 3 4 5 6 7 3 4 5 6 7 8 b) In how many ways can we roll a sum that is divisible by 3? What is the probability of this event? 4 5 6 7 8 9 Second Die . 5 6 7 8 9 10 c) In how many ways can we roll an even sum? :: 6 7 8 9 10 11 d) In how many ways can we roll a sum that is divisible by 3 and even? What is the probability of this event? 7 8 9 10 11 12 e) In how many ways can we roll a sum that is divisible by 3 or even? What is the probability of this event?

Answer 1

Questione e @ 9 = Hold 36 Auswer 02 Sample space, n(s) = 36, E, = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)} No. of ways n() = 6 nie PCE) = nis) Ez = {(1,2), (1,5), (2,1),(2,4), (3,3), (3,6), (4,2), (4,3, (5,1),(5,4),(6,3)/49) No. of ways = n(€2) = 12 n (E₂) P(EZ) = nis) Ez ={(1,1), (1,3), (1,5), (2,2), (2,4),(2,6), (3,1), (3,3), (3,5),(4,2),(4,4),(4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)} No. of ways = n(E3 )= 10 PIE3 ) = Z / Auswer 12 36 . ) 3 Auswa 07 nE3) - 36 nis)

PERN E3 = {(1,5),(2,4),(3,3), (4,2), (5,1),(6,99 sene varma, nieznE3) = 6 = No. of ways n (E2063) nis) = = plezo E3)= 6 36 Auswa ©- & No. of ways =n(E₂ UE3) EU Ez = {(1,1), (1,2),(1,3), (1,5), (2,1),(2,2), (2,4),(2,8),(3,1),(3,3), (3,5), (3,6), (4,2), (4,4),(4,5), (4,6), (5,1),(5,3), (5,4), (5,5), (6,2), (6,3), (6,4), (6,6)} No. of ways n (E₂U E3 ) =24 PLEUE3) n (EZUE3) 24 36 2 3 nis) Auswer