Question

4.tn_3 ap-4
the tree diagram shows all the possible varieties of a t-shirt available in small, medium, and large and in the colors blue and yellow.
what is the probability that a medium t-shirt or a yellow t-shirt is randomly selected? explain.
click the icon to view the tree diagram.

the probability that a medium t-shirt or a yellow t-shirt is randomly selected is $square$. of $square$ possible outcomes, $square$ are either medium, yellow, or both. so, $\triangledown$ = $\triangledown$
(type an integer or a simplified fraction.)

Explanation:

Step1: List all possible outcomes

The T-shirts have 3 sizes (small, medium, large) and 2 colors (blue, yellow), so total outcomes:
$3 \times 2 = 6$
Outcomes: (small, blue), (small, yellow), (medium, blue), (medium, yellow), (large, blue), (large, yellow)

Step2: Identify favorable outcomes

Favorable outcomes are medium (any color) or yellow (any size):
(medium, blue), (medium, yellow), (small, yellow), (large, yellow)
Count of favorable outcomes: $4$

Step3: Calculate probability

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$
$\text{Probability} = \frac{4}{6} = \frac{2}{3}$

Answer:

The probability that a medium T-shirt or a yellow T-shirt is randomly selected is $\frac{2}{3}$. Of 6 possible outcomes, 4 are either medium, yellow, or both. So, $\frac{4}{6} = \frac{2}{3}$