A card is drawn from a deck of 10 cards numbered 1 through 10 and a number cube is rolled. Find each probability.

1. P (10 and 3)

2. P (two even numbers)

3. P (two prime numbers)

4. P (9 and an odd number)

5. P (two numbers less than 4)

6. P (two numbers greater than 5)

1. P (10 and 3) = 1/10 * 1*6 = 1/60.

2. P (two even numbers) = 5/10 * 3/6 = 15/60 = 1/4.

3. P (two prime numbers) = 4/10 * 3/6 = 12/60 = 1/5.

4. P (9 and an odd number) = 1/10 * 3/6 = 3/60 = 1/20.

5. P (two numbers less than 4) = 3/10 * 3/6 = 9/60 = 3/20.

6. P (two numbers greater than 5) = 5/10 * 1/6 = 5/60 = 1/12.

Step-by-step explanation:

The card has the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The number cube has the numbers 1, 2, 3, 4, 5, and 6

In the deck of cards, 5 are odd and 5 are even. Also, there are 4 prime numbers in the deck. Also, there are 3 even and 3 odd numbers on the number cube. Also, there are 3 prime numbers cube. Therefore,

P (Selecting any card from the deck) = 1/10.

P (Any number is rolled on the dice) = 1/6.

Assume that probability of the cards and the cube are independent. So the probabilities can be calculated.

1. P (10 and 3) = 1/10 * 1*6 = 1/60.

2. P (two even numbers) = 5/10 * 3/6 = 15/60 = 1/4.

3. P (two prime numbers) = 4/10 * 3/6 = 12/60 = 1/5.

4. P (9 and an odd number) = 1/10 * 3/6 = 3/60 = 1/20.

5. P (two numbers less than 4) = 3/10 * 3/6 = 9/60 = 3/20.

6. P (two numbers greater than 5) = 5/10 * 1/6 = 5/60 = 1/12.

So the probabilities have been mentioned!