Question

practice

1. ricardo is getting dressed in the dark. he reaches into his sock

drawer to get a pair of socks. he knows that his sock drawer contains
6 pairs of socks, and each pair is a different color. each pair of socks
is folded together. the pairs of socks in the drawer are red, brown,
green, white, black, and blue.

a. how many possible outcomes are there in the experiment?

b. what are the possible outcomes of the experiment?

c. list the sample space for the experiment.

d. calculate ( p(\text{blue}) ).

e. calculate ( p(\text{green}) ).

f. calculate ( p(\text{not red}) ).

g. calculate ( p(\text{not purple}) ).

Explanation:

Step1: Count total sock pairs

Total pairs = 6

Step2: Identify distinct color outcomes

Colors: red, brown, green, white, black, blue

Step3: Define sample space

List all color outcomes

Step4: Calculate P(blue)

Probability = $\frac{\text{Number of blue pairs}}{\text{Total pairs}}$ = $\frac{1}{6}$

Step5: Calculate P(green)

Probability = $\frac{\text{Number of green pairs}}{\text{Total pairs}}$ = $\frac{1}{6}$

Step6: Calculate P(not red)

Probability = $1 - \frac{\text{Number of red pairs}}{\text{Total pairs}}$ = $1 - \frac{1}{6} = \frac{5}{6}$

Step7: Calculate P(not purple)

Probability = $1 - \frac{\text{Number of purple pairs}}{\text{Total pairs}}$ = $1 - 0 = 1$

Answer:

a. 6
b. The possible outcomes are selecting a red pair, a brown pair, a green pair, a white pair, a black pair, or a blue pair of socks.
c. Sample space: {red, brown, green, white, black, blue}
d. $\frac{1}{6}$
e. $\frac{1}{6}$
f. $\frac{5}{6}$
g. $1$