Question
5. Matthew has black socks white socks dress pants, a red shirt, green shirt, and a T-shirt. a) Draw a tree diagram showing his choices for socks, pants , and shirt b) Find the probability that Matthew selects at random i) blue jeans and the T-shirt ii) white socks iii) black socks, dress pants, and a red shirt iv) white socks and not the T -shirt
Solution
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Antonio
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Answer
### a) (A tree diagram would be visually displayed here, branching from socks (black/white) to pants (dress pants) to shirts (red/green/T-shirt).)### b) ### i) 0### ii)
### iii)
### iv)
Explanation
## Step 1: Create the Tree Diagram### Matthew has two choices for socks (black or white), one choice for pants (dress pants), and three choices for shirts (red, green, or T-shirt). We can represent this with a tree diagram. The first branch represents socks, the second branch represents pants, and the third branch represents shirts.## Step 2: Calculate Total Outcomes### Each path from the beginning to the end of the tree diagram represents a possible outcome. There are
total possible outcomes.## Step 3: Calculate Probability of Blue Jeans and T-shirt### The problem states Matthew has dress pants, not blue jeans. Therefore, the probability of choosing blue jeans and a T-shirt is 0.## Step 4: Calculate Probability of White Socks### There are 3 outcomes with white socks out of 6 total outcomes. The probability is
.## Step 5: Calculate Probability of Black Socks, Dress Pants, and Red Shirt### There is 1 outcome with black socks, dress pants, and a red shirt out of 6 total outcomes. The probability is
.## Step 6: Calculate Probability of White Socks and Not a T-shirt### There are 2 outcomes with white socks and not a T-shirt (white socks with red shirt and white socks with green shirt) out of 6 total outcomes. The probability is
.