Drawing a least one king when you draw a card from a standard deck 8 times (replacing the card each time you draw, so there are always 52 cards in the deck)
P(at least one king in 8 attempts)= [P(1 king + 2 kings + 3 kings + 4 kings]^8 =
1/52 + 2/52 + 3/52 + 4/52 = 10/52^8
Not sure how to solve, should I subtract 1 from the answer.
Drawing at least one ten when you draw a card from a standard deck 9 times (replacing the card each time you draw)
Well, if you want to find the probability of drawing at least one king in 8 attempts, you can use the concept of complementary probability. This means that you find the probability of the opposite event (in this case, drawing no kings), and subtract it from 1.
The probability of not drawing a king in one attempt is 48/52, since there are 48 non-king cards out of 52 in the deck. Therefore, the probability of not drawing a king in 8 attempts is (48/52)^8.
To find the probability of drawing at least one king, you subtract this probability from 1:
P(at least one king) = 1 - P(no kings)
P(at least one king) = 1 - (48/52)^8
So, you don't have to subtract 1 from the answer, this equation will give you the probability of drawing at least one king in 8 attempts.
To find the probability of drawing at least one king in 8 attempts, you can use the approach of finding the complement event and subtracting it from 1. The complement event is the probability of not drawing any king in 8 attempts.
The probability of not drawing a king in one attempt is 48/52, since there are 4 kings in a standard deck of 52 cards. Since you are replacing the card after each draw, the probability remains the same for each attempt.
To find the probability of not drawing a king in 8 attempts, you can multiply the probabilities for each attempt:
(48/52)^8
Then, subtract this probability from 1 to find the probability of drawing at least one king in 8 attempts:
1 - (48/52)^8
This will give you the final answer.
To calculate the probability of drawing at least one king in 8 attempts with replacement, you need to consider the complement of the event (i.e., the probability of not drawing a king in any of the 8 attempts) and subtract it from 1.
The probability of not drawing a king in a single attempt is given by:
P(no king) = 48/52 (since there are 48 non-king cards in the deck, and 52 total cards).
Since each attempt is independent (you replace the card each time), you can use this probability for all 8 attempts. Therefore, the probability of not drawing a king in all 8 attempts is:
P(no king in 8 attempts) = (48/52)^8
Now, to find the probability of drawing at least one king, you subtract the probability of not drawing a king from 1:
P(at least one king in 8 attempts) = 1 - P(no king in 8 attempts)
Therefore, the final calculation becomes:
P(at least one king in 8 attempts) = 1 - (48/52)^8
You do not need to subtract 1 from the answer since we already considered the complement when calculating the probability of not drawing a king in 8 attempts.
prob(a king) = 4/52 = 1/13
prob(not a king) = 12/13
let's find the prob of NOT getting a king, 8 times in a row
= (12/13)^8
but we DON'T want that to happen
so prob of at least one king somewhere
= 1 - (12/13)^8
= appr .4729
btw, your attempt makes no sense to me