The probability of guessing the correct answers to certain question is x/2. If the probability of not guessing the correct answer to the question is 2/3 ,what is the value of x.?

Question

Answer

Given ;             Probability of correct ans = x/2 nd nd probability of incorrect ans = ⅔. To find ;               value of x. Solution ;             x/2 + ⅔  =   1.......             3x + 4 / 6 =  1......              3x + 4       =   1*6               3x  =    6 -  4               3x  =   2                  x =    ⅔

Answer

0.5

Answer

Understanding the Problem
To find the value of x, we need to analyze the probabilities given in the problem.
Given Information
- The probability of guessing the correct answer is x/2.
- The probability of not guessing the correct answer is 2/3.
Relationship Between Probabilities
The probability of an event and its complement (not occurring) adds up to 1. Therefore, we can write the following equation:
- Probability of guessing the correct answer + Probability of not guessing the correct answer = 1
Setting Up the Equation
Using the information provided:
- (x/2) + (2/3) = 1
Finding a Common Denominator
To solve for x, we first need a common denominator for the fractions. The least common multiple of 2 and 3 is 6.
- Convert x/2 to a fraction with a denominator of 6:
- (x/2) = (3x/6)
- Convert 2/3 to a fraction with a denominator of 6:
- (2/3) = (4/6)
Substituting Back Into the Equation
Now we can rewrite the equation:
- (3x/6) + (4/6) = 1
Simplifying the Equation
Multiply both sides by 6 to eliminate the denominator:
- 3x + 4 = 6
Solving for x
Now isolate x:
- 3x = 2
- x = 2/3
Conclusion
The value of x is 2/3. This represents the probability of guessing the correct answer expressed in the form required.

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Similar Class 9 Doubts

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