Question

There is a stack of 8 cards, each given a different number from 1 to 8. 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 even number and the second card is greater than

6? Write your answer as a fraction in simplest form.

Answer 1

Here, Total Outcome = 8 [ For both operations ]

Number which are even between 1 & 8 = 2, 4, 6, 8
So, the probability would be: 4/8 = 1/2

Numbers which are greater than 6 = 7, 8
So, the probability would be: 2/8 = 1/4

Now, In order to have a combined probability you need to multiply the numbers, = 1/2 * 1/4 = 1/8

In short, Your Answer would be 1/8

Hope this helps!

Answer 2

The probability of drawing an even number is 4/8 = 1/2 since there are 4 even cards (2,4,6,8) out of 8 total.

After the first draw, the card is put back. There are still 8 cards in the deck. There are 2 cards that are larger than 6. Those numbers are 7 and 8. So the probability of picking a card larger than 6 is 2/8 = 1/4

Multiply the two individual probabilities to get
(1/2)*(1/4) = (1*1)/(2*4) = 1/8

The final answer is 1/8