Question

Rasheed 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 six 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(blue).



E. Calculate P(not purple)

Answer 1

Part A: There are 6 possible outcomes of this experiment.

Part B: There are 6 possible outcomes of the experiment ; red, brown, green, white, black, and blue ( equal)

Part C:

Sample Space = { red, brown, green, white, black, blue }

Part D:

P (blue)= 1/6

Part E:

P (not purple)= 1

Explanation:

Part A:

There are 6 possible outcomes of this experiment.

As there are 6 pairs of socks. Each pair is folded together so that the socks cannot be mixed up . There is 1 chance of choosing each pair of socks.

Part B:

The chosen socks can be any of the following red, brown, green, white, black, and blue so there are 6 possible outcomes of the experiment ; red, brown, green, white, black, and blue (all have equal probability) .

Part C:

The sample space contains all the possible outcomes of the event.

Sample Space = { red, brown, green, white, black, blue }

Part D:

P(blue)= No of favorable outcomes/ Total no of outcomes

P (blue)= 1/6

Part E:

P (not purple)= 1

As the total probability is always equal to 1 and we want to find the probability of the color which is not given in the list

P( purple) = 0/6= 0

And the probability of not purple is given by the formula

P (not purple) = 1- P (purple)

= 1-0= 1

1 indicates that the event of any other color except purple must occur which is equal to the probability of not purple.

This can be solved by complement rule also.