Question of the Day

Can you answer today's question?

Register Next Tests:
10/11 , 11/8

Jul
15
2013
196,132 responses
Question of the Day Statistics
Number Answered
Correct 93,784
Incorrect 102,348
47% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

A 6-sided number cube, with faces numbered 1 through 6, is to be rolled twice. What is the probability that the number that comes up on the first roll will be less than the number that comes up on the second roll?

Answer Choices

Hint

For the two numbers that will come up there are three possibilities:

  •    The first number is less than the second
  •    They are equal
  •    The first number is greater than the second

Question of the Day

Can you answer today's question?

Register Next Tests:
10/11 , 11/8

Jul
15
2013
196,132 responses
Question of the Day Statistics
Number Answered
Correct 93,784
Incorrect 102,348
47% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

A 6-sided number cube, with faces numbered 1 through 6, is to be rolled twice. What is the probability that the number that comes up on the first roll will be less than the number that comes up on the second roll?

Answer Choices

Answer

The outcome space for this experiment is the set of all ordered pairs (a comma b) where a represents the first number that comes up, and b represents the second one. Since a and b can take all the values 1 through 6, there will be a total of 36 possible outcomes. The outcomes can be represented in a table as shown:

graphic

Among all the pairs (a comma b), 6 are pairs for which a = b. So 30 remaining pairs will have a not equal to b. Notice that the number of pairs  (a comma b) for which a less than b is the same with the number of pairs 

(a comma b) for which a greater than b. Therefore the number of pairs 

(a comma b) for which a less than b, is 15(half of 30). Then the probability that a less than b is equal to (number of pairs (a comma b) comma where a less than b) over (number of all possible outcomes) = 15 over 36 = 5 over 12.