Please this problem to me

There is a stack of 8 cards from 1-8 suppose we select a card randomly from the stack, replace it, then randomly select another card What is the probability the first card is a even number and the second card is greater than 6 write answer in simplest from

To find the probability that the first card is an even number and the second card is greater than 6, we need to determine the total number of possible outcomes and the number of favorable outcomes.

First, let's calculate the total number of possible outcomes. Since we are selecting cards randomly from a stack of 8 cards, the total number of possible outcomes is 8.

Next, let's determine the number of favorable outcomes. There are 4 even numbers (2, 4, 6, and 8) in the stack, and there are 2 numbers greater than 6 (7 and 8) in the stack. Thus, there are 4 even numbers and 2 numbers greater than 6, and the number of favorable outcomes is 4 * 2 = 8.

Therefore, the probability of selecting an even number first and a number greater than 6 second is 8/8 = 1.

To find the probability, we need to first determine the total number of possible outcomes, as well as the number of favorable outcomes.

Total number of possible outcomes:
Since we select one card from a stack of 8 cards (numbers 1 to 8) and replace it before selecting the second card, there are 8 possible choices for each selection. Therefore, the total number of possible outcomes is 8 * 8 = 64.

Number of favorable outcomes:
We want to find the probability that the first card is an even number and the second card is greater than 6.

Even numbers in the stack of cards are 2, 4, 6, and 8. There are 4 possible even numbers.

Numbers greater than 6 in the stack of cards are 7 and 8. There are 2 possible numbers greater than 6.

Since we are selecting the cards with replacement, the probability of selecting an even number on the first card is 4/8 = 1/2.
The probability of selecting a number greater than 6 on the second card is 2/8 = 1/4.

To find the probability of both events occurring, we multiply the individual probabilities:
(1/2) * (1/4) = 1/8.

Therefore, the probability that the first card is an even number and the second card is greater than 6 is 1/8.

The first possibility :

First : 8 = > 1
Monday : 7 = > 1
Total 1 case
The second possibility
First : 2,4,6
Second: 7.8
Total : 3x2 = 6 case
Overall both cases = 7
Probability : 7 / ( 8C2 ) = 0.25 - > 25 %