Question

The numbers 3, 4, 5, and 7 are written on separate pieces of paper and put into a hat. Two pieces of paper are drawn at the same time and the product of the numbers is recorded. Find the sample space.

Answer 1

The sample space for drawing two numbers from the set {3, 4, 5, 7} and recording their product consists of all unique pairs that can be drawn: {12, 15, 21, 20, 28, 35}.

Step-by-step explanation:

The question involves finding the sample space for drawing two numbers from a set and recording their product. The numbers given are 3, 4, 5, and 7. We draw two numbers at a time without replacement, meaning the same number cannot be picked twice. The sample space can be constructed by listing all possible unique pairs and then calculating their products. Here are the pairs and their products:

• (3, 4) with a product of 3×4 = 12
• (3, 5) with a product of 3×5 = 15
• (3, 7) with a product of 3×7 = 21
• (4, 5) with a product of 4×5 = 20
• (4, 7) with a product of 4×7 = 28
• (5, 7) with a product of 5×7 = 35

Therefore, the sample space is {12, 15, 21, 20, 28, 35}.

Answer 2

the final sample space is { 12,15,20,21,28,35}

Step-by-step explanation:

the sample space is the set of possible outcomes of the experiment , then the possible products are

3*7 = 21

3*5 = 15

3*4 = 12

4*7 = 28

4*5 = 20

5*7 = 35

since the product of 2 numbers is commutative, then we do not count the other possible combinations

therefore the final sample space is { 12,15,20,21,28,35}

Note:

to check that we have all the products , the possible combinations are

C(4,2)= 4!/(4-2)!*2!= 3*2*1 = 6

since we have considered 6 products , we are sure that our result is correct