Question

IM GIVING 40 POINTS!

There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is less than 4? Write your answer as a fraction in the simplest form

Answer 1

3/20.

Explanation:

To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is:

5/10 x 3/10 = 15/100

We can simplify this fraction by dividing both the numerator and denominator by 5:

15/100 = 3/20

So, the final answer is 3/20.

Received message. To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is: 5/10 x 3/10 = 15/100 We can simplify this fraction by dividing both the numerator and denominator by 5: 15/100 = 3/20 So, the final answer is 3/20.

Answer 2

There are 10 cards in the stack, and 5 of them are odd (1, 3, 5, 7, and 9). There are 3 cards (1, 2, and 3) that are less than 4. Since we are replacing the first card before selecting the second, the outcomes are independent and we can multiply the probabilities of each event.

The probability of selecting an odd card on the first draw is 5/10, or 1/2.

The probability of selecting a card less than 4 on the second draw is 3/10, since there are 3 cards that meet this condition out of a total of 10.

Therefore, the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is:

(1/2) x (3/10) = 3/20

So the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is 3/20.

Explanation: