Question

Solve this question with valid reason and also make the table ​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{ANSWER}}}}}}$

Given:

• 2 dice are thrown and the sum of the numbers obtained is noted
• Numbers on 1st die = 1,2,3,4,5,6
• Numbers on 2nd die = 1,1,2,2,3,3

To Find:

• Probability of getting each sum from 2 to 9 separately

Outcomes:

$\large{\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6}\sf(1,1)&\sf(2,1)&\sf(3,1)&\sf(4,1)&\sf(5,1)&\sf(6,1) \\\cline{1-6}\sf(1,1)&\sf(2,1)&\sf(3,1)&\sf(4,1)&\sf(5,1)&\sf(6,1) \\\cline{1-6}\sf(1,2)&\sf(2,2)&\sf(3,2)&\sf(4,2)&\sf(5,2)&\sf(6,2) \\\cline{1-6}\sf(1,2)&\sf(2,2)&\sf(3,2)&\sf(4,2)&\sf(5,2)&\sf(6,2) \\\cline{1-6}\sf(1,3)&\sf(2,3)&\sf(3,3)&\sf(4,3)&\sf(5,3)&\sf(6,3) \\\cline{1-6}\sf(1,3)&\sf(2,3)&\sf(3,3)&\sf(4,3)&\sf(5,3)&\sf(6,3) \\\cline{1-6}\end{tabular}}$

Solution:

Total outcomes = 36

Probability = (Favourable outcomes)/(Total Outcomes)

1. Outcomes with sum = 2

⇒ (1,1) ; (1,1)

⇒ No of. Favourable outcomes = 2

⇒ Probability = 2/36 = 1/18

2. Outcomes with sum = 3

⇒ (1,2) ; (1,2) ; (2,1) ; (2,1)

⇒ No of. Favourable outcomes = 4

⇒ Probability = 4/36 = 1/9

3. Outcomes with sum = 4

⇒ (1,3) ; (1,3) ; (2,2) ; (2,2) ; (3,1) ; (3,1)

⇒ No of. Favourable outcomes = 6

⇒ Probability = 6/36 = 1/6

4. Outcomes with sum = 5

⇒ (2,3) ; (2,3) ; (3,2) ; (3,2) ; (4,1) ; (4,1)

⇒ No of. Favourable outcomes = 6

⇒ Probability = 6/36 = 1/6

5. Outcomes with sum = 6

⇒ (3,3) ; (3,3) ; (4,2) ; (4,2) ; (5,1) ; (5,1)

⇒ No of. Favourable outcomes = 2

⇒ Probability = 6/36 = 1/6

6. Outcomes with sum = 7

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

⇒ No of. Favourable outcomes = 6

⇒ Probability = 6/36 = 1/6

7. Outcomes with sum = 8

⇒ (5,3) ; (5,3) ; (6,2) ; (6,2)

⇒ No of. Favourable outcomes = 4

⇒ Probability = 4/36 = 1/9

8. Outcomes with sum = 9

⇒ (6,3) ; (6,3)

⇒ No of. Favourable outcomes = 2

⇒ Probability = 2/36 = 1/18

Formula Used:

• Probability = (Favourable outcomes)/(Total Outcomes)

Answer 2

Outcome with sum 2

probability =1/8

Outcome with sum 3

probability =1/9

outcome with sum 4

probability =1/6