Question

an item is randomly drawn from a bag with 17 red marbles, 8 green marbles, 13 red beans, and 7 blue beans.
event a: red
event b: marble
\\(p(a \text{ or } b) = ? \\)
hint: \\(p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b)\\)
round your answer to the nearest hundredth.

Explanation:

Calculate total items

Using the Theoretical Probability knowledge point

$$ \text{Total} = 17 \text{ (red marbles)} + 8 \text{ (green marbles)} + 13 \text{ (red beans)} + 7 \text{ (blue beans)} = 45 $$

Find individual probabilities

Using the Theoretical Probability knowledge point

$$
LATEXBLOCK0
$$

Find intersection probability

Using the Overlapping Events knowledge point

$$ P(A \text{ and } B) = P(\text{red marble}) = \frac{17}{45} $$

Apply addition rule

Using the Overlapping Events knowledge point

$$ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) = \frac{30}{45} + \frac{25}{45} - \frac{17}{45} = \frac{38}{45} $$

Convert to decimal

Using the Theoretical Probability knowledge point

$$ P(A \text{ or } B) = \frac{38}{45} \approx 0.8444... \approx 0.84 $$

Answer:

An item is randomly drawn from a bag with 17 red marbles, 8 green marbles, 13 red beans, and 7 blue beans.
Event A: red
Event B: marble
\(P(A \text{ or } B) =\) <blank>0.84</blank>