Question

Two dice are rolled simultaneously. Find the probability that
(i) the sum of the numbers on their upper faces is at the most 5.
(ii) the sum of the numbers on their upper faces is at the least 6.​

Answer 1

Answer:

Hey buddy here's ur answer..

1. 5/18
2. 5/9

Step-by-step explanation:

when 2 dices are rolled simultaneously,

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);(5,6)

( 6,1);(6,2);(6,3);(6,4);(6,5);(6,6)}

n(S)=36

1)Let A be the probability when the sum of the numbers on their upper faces is at the most 5

so,A = {(1,1);(1,2);(1,3);(1,4);(2,1);(2,2);(2,3);(3,1);(3,2);(4,1)}

n(A)=10

P(A)=n(A)/n(S)

=10/36

=5/18

2)Let B be the probability when sum of the numbers on their upper faces is at the least 6

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

n(B)=20

P(B)=n(B)/n(S)

=20/36

=5/9

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Answer 2

1. 5/18

2. 13/18

Step-by-step explanation:

when 2 dices are rolled simultaneously,

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);(5,6),

(6,1);(6,2);(6,3);(6,4);(6,5),(6,6)}

n(S)=36

1) Let A be the probability when the sum of the numbers on their upper faces is at the most 5

ANSWER

At the most means it can be less than 5 but not more than 5

Event A : {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)}

n(A) = 10

P(A)= n(A)/ n(S)

= 10 / 36

= 5 / 18

P(A) = 5 / 18

2) Let B be the probability when the sum in the upper face is at least 6

At the least means it can be 6 or more

than 6

Event B: {(1,5), (1,6), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (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(B) = 26

P(B) = n(B)/ n(S)

= 26 / 36

= 13/18

P(B) = 13 / 18

Thank you