The numbers 1-10 are written on note cards and placed in a bag. One card will be drawn from the bag at random..

List the sample space for this experiment.

Are the events selecting an even number and selecting an odd number equally likely? Explain.

Are the events selecting a number divisible by 3 and selecting a number divisible by 5 equally likely? Explain.

Sample space: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Yes, both have 50% probability

No, first event has 30% probability and second one has 20% probability

Step-by-step explanation:

As we have a total of 10 note cards, each if a number from 1 to 10 (each card with a different number) and we want to draw one card at random, the sample space is each of the 10 numbers in the note (sample space with 10 elements):

1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

From this 10 numbers, we have a total of 5 odd numbers and 5 even numbers, so the events of selecting an even number and selecting an odd number are equally likely (the probability of both events are 5/10 = 50%)

The numbers from the sample space divisible by 3 are:

3, 6, 9 (so a total of 3 elements, probability of 3/10 = 30%)

The numbers from the sample space divisible by 5 are:

5, 10 (so a total of 2  elements, probability of 2/10 = 20%)

As the probabilities are different, these events are not equally likely