NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 39
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 39
A die has faces 0,1,1,1,6,6. Two such dice are thrown and total score recorded. (i) How many different totals possible? (ii) Probability of a total of 7?
Answer:
(i) 6 totals (0,1,2,6,7,12); (ii) \(\dfrac{1}{3}\)
Detailed Answer with Explanation:
Step 1: Understand the die.
The die has 6 faces: 0, 1, 1, 1, 6, 6. That means: one face shows 0, three faces show 1, and two faces show 6.
Step 2: Totals when two dice are thrown.
We add the numbers on both dice to get the total.
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 1 = 2
- 0 + 6 = 6
- 1 + 6 = 7
- 6 + 6 = 12
So, the different totals possible are: 0, 1, 2, 6, 7, 12. That makes 6 totals.
Step 3: Probability of total = 7.
To get a total of 7, one die must show 1 and the other die must show 6.
- Case A: First die shows 1, second die shows 6.
- Case B: First die shows 6, second die shows 1.
Step 4: Count favourable outcomes.
Probability of 1 on one die = 3/6 (since 3 faces have 1). Probability of 6 on one die = 2/6 (since 2 faces have 6).
For Case A: (3/6) × (2/6) = 6/36
For Case B: (2/6) × (3/6) = 6/36
Total favourable = 6/36 + 6/36 = 12/36.
Step 5: Simplify.
12/36 = 1/3.
Final Answer:
(i) 6 totals possible. (ii) Probability of 7 = 1/3.