you have a math test to and it will contain both multiple-choice questions and free- response questions.The test is total of 50
2 answers:
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Answer:
The probability that his coloring is factorific is 0.28125
Step-by-step explanation:
For calculate the probability is necessary to identify the total number of ways to color the six number. This can be calculate with the rule of multiplication as:
2*2*2*2*2*2=64
Because we have 2 options to color every number.
For know the number of ways in which the coloring is factorific, first we need to identify the divisors of each number:
1: the divisor is 1
2: The divisors are 2 and 1
3: The divisors are 3 and 1
4: The divisors are 4, 2 and 1
5: The divisors are 5 and 1
6: The divisors are 6, 3 and 1
From these information we analyse that for made a factorific coloring, is necessary that the number 1 is color blue. Additionally if the number 4 is color blue, the number 2 needs to be color blue and if the number 6 is blue, the number 3 needs to be blue.
So, the number of ways in which we can create a factorfic number is determined by the following cases:
- The number 2 is blue and the number 3 is blue: In this case we have 1 option for number 1, one for number 2 and 1 for number 3. Taking into account that the number 2 and 3 are blue, if the number 4 and 6 are blue or red doesn't change the fact that the coloring is going to be factorific. So, we have two options for number 3 and 2 options for number 6. Finally the color of the number 5 is independent of the colors of number 2 and 3, so we also have 2 options for coloring number 5 and the coloring is going to be factorific. Then the number of ways for this situation is calculate as:
<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 2 </u> *<u> 2 </u>* <u> 2 </u>= 8
number 1 number 2 number 3 number 4 number 5 number 6
At the same way we can calculate the following cases:
- The number 2 is blue and the number 3 is red: If the number 3 is red, the coloring is only going to be factorific is number 6 is red. Then the number of ways for this situation is calculate as:
<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 2 </u> *<u> 2 </u>* <u> 1 </u>= 4
number 1 number 2 number 3 number 4 number 5 number 6
- The number 2 is red and the number 3 is red: If the number 2 and 3 are red, the coloring is only going to be factorific is number 4 and 6 are red. Then the number of ways for this situation is calculate as:
<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 1 </u> *<u> 2 </u>* <u> 1 </u>= 2
number 1 number 2 number 3 number 4 number 5 number 6
- The number 2 is red and the number 3 is blue: If the number 2 is red, the coloring is only going to be factorific is number 4 is red. Then the number of ways for this situation is calculate as:
<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 1 </u> *<u> 2 </u>* <u> 2 </u>= 4
number 1 number 2 number 3 number 4 number 5 number 6
If we sum all the cases, we obtain 18 ways to make a factorific coloring. So the probability can be calculated as: