Question

two events, x and y, are independent of each other. ( p(y)=\frac{5}{6} ) and ( p(x \text{ and } y)=\frac{1}{3} ). what is ( p(x) ) written as a decimal? round to the nearest tenth, if necessary. options: 0.2, 0.3, 0.4, 0.5

Explanation:

Step1: Recall the formula for independent events

For independent events \( X \) and \( Y \), the probability of both occurring is \( P(X \text{ and } Y) = P(X) \times P(Y) \).

Step2: Substitute the known values into the formula

We know \( P(Y) = \frac{5}{6} \) and \( P(X \text{ and } Y) = \frac{1}{3} \). Let \( P(X) = p \). Then:

$$ \frac{1}{3} = p \times \frac{5}{6} $$

Step3: Solve for \( p \)

To solve for \( p \), we can rearrange the equation:

$$ p = \frac{\frac{1}{3}}{\frac{5}{6}} $$

Dividing by a fraction is the same as multiplying by its reciprocal:

$$ p = \frac{1}{3} \times \frac{6}{5} = \frac{6}{15} = \frac{2}{5} $$

Step4: Convert the fraction to a decimal

\( \frac{2}{5} = 0.4 \)

Answer:

0.4