Question

Two different dice are thrown simultaneously. Find the probability if getting:

1. sum 7

ii. sum ≤ 3

iii. sum ≤ 10​

Answer 1

Answer:

1) sum 7

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

2) sum < = 3. = {(1,1),(1,2),(2,1)}= 3

3)sum of < = 10. = {(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),(3,2),(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),

(6,1),(6,2),(6,3),(6,4) = 26

Answer 2

Answer:

i) 1/6 ii) 1/12 iii) 11/12

Step-by-step explanation:

1)Cases favorable to an even no's are the sum

(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)

Total no of outcomes =36

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

Total no of outcomes = 6

P(sum 7) = 6/36 =1/6   ( ÷ by 6)

P=1/6

ii) S = { (1,1),(1,2),(2,1) }

Total no of outcomes = 3

P(sum less than or equal to 3) = 3/36  

P = 1/12  ( ÷ by 3)

iii) S = { (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),

(6,1),(6,2),(6,3),(6,4)}

Total no of outcomes = 33

P(sum less than or equal to 10) = 33/36 ( ÷ by 3)

P = 11/12