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 or b) =? hint: p(a or b) = p(a) + p(b) - p(a and b) round your answer to the nearest hundredth.

Explanation:

Step1: Calculate total number of items

$17 + 8+13 + 7=45$

Step2: Calculate P(A)

The number of red items is $17 + 13=30$. So $P(A)=\frac{30}{45}=\frac{2}{3}$

Step3: Calculate P(B)

The number of marbles is $17 + 8 = 25$. So $P(B)=\frac{25}{45}=\frac{5}{9}$

Step4: Calculate P(A and B)

The number of red - marbles is 17. So $P(A\ and\ B)=\frac{17}{45}$

Step5: Calculate P(A or B)

Using the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$, we substitute the values:
$P(A\ or\ B)=\frac{2}{3}+\frac{5}{9}-\frac{17}{45}$
$=\frac{30 + 25-17}{45}=\frac{38}{45}\approx0.84$

Answer:

$0.84$