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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) ​

Respuesta :

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Answer:

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!!!

The respective probabilities for the number for the cube and cards are; as gotten below.

What is the probability?

We are told that;

- 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

- Contents of the deck of cards; 5 are odd, 5 even, 4 prime numbers in the deck.

- There are 3 even and 3 odd numbers on the number cube with 3 prime numbers cube.

Thus the respective probabilities are;

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.

Read more about Probability at; https://brainly.com/question/251701

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