Determine the probability of drawing socks from a drawer of 8 black socks, 6 blue socks, and 4 white socks without replacement.

Question

Determine the probability of drawing socks from a drawer of 8 black socks, 6 blue socks, and 4 white socks without replacement.

 

a. drawing a blue sock, then a black sock​​​​​​​​ __________

 

b. drawing a black sock, then a black sock​​​​​​​​ ___________

 

Answer 1

In probability, When an item is chosen, we refer to the total number of that item in the sample space. The sample space is the total number of events/item that are available.

In the question above, the sample space 8 + 6 + 4 = 18

In an event of drawing an item, the item drawn will take care of that number of items over the sample space for instance, if Black socks is drawn, we will ask how many black socks do we have? and the answer is 8 black socks. Therefore the probability is 8/18

In some cases, where two or more items are drawn, we ask whether has the item been replaced or not, if replace then, the Probability will be First event/sample space * second event/sample space. for example, one black and then one blue with replace.

8/18 * 6/18 = 0.1481

what if the first item has not been replaced, then it means that the sample space will reduce by 1 because one black has been taken out.

8/18 * 6/17 = 0.1569

Now the solution.

a. 6/18 * 8/17 = 0.1569

b. 8/18 * 7/17 = 0.1830

Remember that if same colour is chosen the second time then, that particular item has reduced from its original stage by deducting 1 from the old balance.