Question

If the probability of guessing the correct answer to a question is \(\frac {x}{12}\) and the probability of not guessing the correct answer is \(\frac 58\), the value of \(x\) is

• A. 4.5
• B. 4
• C. 1.2
• D. 0.5

Answer 1

The Correct Option is A

We are given that $$ P(\text{correct}) = \frac{x}{12} $$ and $$ P(\text{not correct}) = \frac{5}{8} $$ 

We know that the sum of the probabilities of all possible outcomes is 1. 

In this case, the only possible outcomes are guessing the correct answer or not guessing the correct answer. 

Thus, $$ P(\text{correct}) + P(\text{not correct}) = 1 $$ $$ \frac{x}{12} + \frac{5}{8} = 1 $$ 

To solve for $x$, we can first subtract $\frac{5}{8}$ from both sides: $$ \frac{x}{12} = 1 - \frac{5}{8} = \frac{8}{8} - \frac{5}{8} = \frac{3}{8} $$ Now, multiply both sides by 12 to isolate $x$: $$ x = 12 \cdot \frac{3}{8} = \frac{12 \cdot 3}{8} = \frac{36}{8} = \frac{9}{2} = 4.5 $$ 

Therefore, the value of $x$ is 4.5.