For all probabilities, show work, round decimal answers to 3 decimal places and percent answers to 1 decimal.
$Unknown environment 'tabular'$
3. A bag contains two shapes, and each shape can be one of three colors. The two-way table above shows the frequency of each shape.
What is the probability of randomly choosing a green shape?
$Unknown environment 'tabular'$
What is the probability of randomly choosing a red shape and it is a circle?
$Unknown environment 'tabular'$
What is the probability of randomly choosing a blue or red shape?
$Unknown environment 'tabular'$
What is the probability of randomly choosing an item that is red or a triangle?
$Unknown environment 'tabular'$
Assuming the item you select is green, what is the probability it is a circle?
$Unknown environment 'tabular'$
What is the probability of choosing a blue circle, returning it, and then choosing a blue triangle?
$Unknown environment 'tabular'$
If you chose two objects in a row and did not return either of them, what is the probability they are both blue?
$Unknown environment 'tabular'$

Answer

Expert–verified

Hide Steps

Answer

$P (Both blue, no return) = \frac{10}{35} \cdot \frac{9}{34}$ $\approx 0.075$ $\approx 7.5 %$

Steps

Step 1 ： $P (Green shape) = \frac{16}{35}$ $\approx 0.457$ $\approx 45.7 %$

Step 2 ： $P (Red circle) = \frac{4}{35}$ $\approx 0.114$ $\approx 11.4 %$

Step 3 ： $P (Blue or Red shape) = \frac{13 + 6}{35}$ $\approx 0.543$ $\approx 54.3 %$

Step 4 ： $P (Red or Triangle) = \frac{6 + 12}{35}$ $\approx 0.514$ $\approx 51.4 %$

Step 5 ： $P (Circle | Green) = \frac{9}{16}$ $\approx 0.562$ $\approx 56.2 %$

Step 6 ： $P (Blue circle, return, Blue triangle) = \frac{10}{35} \cdot \frac{3}{35}$ $\approx 0.008$ $\approx 0.8 %$

Step 7 ： $P (Both blue, no return) = \frac{10}{35} \cdot \frac{9}{34}$ $\approx 0.075$ $\approx 7.5 %$