Question

In a hat, you have index cards with the numbers 1 through 10 written on them. Find how many of the 10 possible numbers you can pick match the described event, then drag and drop each of the numbers into the correct box to order the events from least likely to happen (1) to most likely to happen (8) when you pick one card at random.

A. You pick a number greater than 0. B. You pick an even number. C. You pick a number that is at least 2. D. You pick a number that is at most 0. E. You pick a number divisible by 3. F. You pick a number divisible by 5. G. You pick a prime number. H. You pick a number less than the greatest prime number among the
numbers 1 through 10.

Answer 1

8,5.7,1,3,2,4,6 is the correct order

Explanation:

1. There are 10 numbers from 1 to 10 , thus there are 10 possible outcomes.

Determine the number of favourable outcomes for each event:

Number greater than 0 : 10 favourable outcomes ( 1,2,3,4,5,6,7,8,9,10)

Even number : 5 favourable outcomes ( 2,4,6,8,10)

Number is at least 2 : 9 favourable outcomes ( 2,3,4,5,6,7,8,9,10)

Number is at most 0 : 0 favourable outcomes ( as none of the integers from 1 to 10 are at most 0 )

Number is divisible by 3 : 3 favourable outcomes ( 3, 6,9)

Number is divisible by 5 : 2 favourable outcomes ( 5, 10)

Prime number : 4 favourable outcomes ( 2, 3, 5, 7 )

Number less than the greatest prime number : 6 favourable outcomes ( 1, 2,3,4,5,6 as 7 is the greatest prime number from the numbers of 1 to 10 )

2. The more favourable outcomes correspond with an event, the more likely the event is to happen. Thus the number is at most 0 is the least likely and the number greater than 0 is the most likely.

Let us then number the events from least likely to most likely:

Number greater than 0: 8

Even number: 5

Number is at least 2: 7

Number is at most 0:1

Number is divisible by 3: 3

Number is divisible by 5: 2

Prime number 4

Number less than the greatest prime number: 6

So the order is 8,5.7,1,3,2,4,6