Question

you pick a card at random, put it back, and then pick another card at random. 5,6,7,8 what is the probability of picking 6 then picking an even number?

Answer 1

Explanation:

if I understand correctly, we have 4 cards to pick from :

5, 6, 7, 8

my answer bases on that understanding.

a probability is always the ratio

desired cases / totally possible cases.

so, the probability to pick 6 is simply

1/4 = 0.25

1 desired card out of 4 possible cards.

then we would have 3 cards left, but we put the picked card back and have all 4 cards available for the second pick.

the probability of picking an even number is

2/4 = 1/2 = 0.5

6 and 8 are the desired cases out of the 4 possible cards.

now we combine both single (and independent !) events into one connected event.

for an AND relationship (both things happen) we multiply the 2 probabilities.

for an OR relationship (one of the two things happens) we add the 2 probabilities.

in our case both need to happen.

so, the probability for that is

1/4 × 1/2 = 1/8 = 0.125