A fair dice is rolled. Probability of getting a number x such that 1 &...
A fair dice has six faces numbered 1, 2, 3, 4, 5, 6, and each outcome is equally likely.
Given Condition:
We need to find the probability of getting a number x such that 1 ≤ x ≤ 6.
Step 1: Number of favorable outcomes
The possible outcomes for x satisfying 1 ≤ x ≤ 6 are 1, 2, 3, 4, 5, 6. This gives a total of 6 favorable outcomes.
Step 2: Total possible outcomes
When a fair dice is rolled, there are 6 total possible outcomes.
Step 3: Probability formula
Probability = (Number of favorable outcomes) / (Total possible outcomes)
Probability = 6 / 6 = 1
A fair dice is rolled. Probability of getting a number x such that 1 &...
Understanding the Problem
When a fair die is rolled, it can land on any of the six faces, which are numbered from 1 to 6. The question asks for the probability of rolling a number x such that 1 < x="" />< 6.="" />Identifying the Valid Outcomes
- The numbers that satisfy the condition 1 < x="" />< 6="" are:="" -="" 2="" -="" 3="" -="" 4="" -="" 5="" />Counting the Successful Outcomes
- There are four successful outcomes (2, 3, 4, 5) that meet the criteria.
Total Possible Outcomes
- A die has a total of six outcomes (1, 2, 3, 4, 5, 6).
Calculating the Probability
- The probability of an event is calculated as:
- Probability = (Number of Successful Outcomes) / (Total Possible Outcomes)
- In this case:
- Successful Outcomes = 4 (which are 2, 3, 4, 5)
- Total Outcomes = 6
- Therefore, Probability = 4/6 = 2/3
Conclusion
- The probability of rolling a number x such that 1 < x="" />< 6="" is="" not="" 1,="" but="" rather="" 2/3,="" which="" falls="" between="" 0="" and="" />
thus, the correct answer is option c) between 0 and 1.
this showcases the importance of understanding the range of valid outcomes when dealing with probability questions. 6="" is="" not="" 1,="" but="" rather="" 2/3,="" which="" falls="" between="" 0="" and="" 1.="" thus,="" the="" correct="" answer="" is="" option="" c)="" between="" 0="" and="" 1.="" this="" showcases="" the="" importance="" of="" understanding="" the="" range="" of="" valid="" outcomes="" when="" dealing="" with="" probability="">
thus, the correct answer is option c) between 0 and 1.
this showcases the importance of understanding the range of valid outcomes when dealing with probability questions.>