Drawing at least one queen when you draw a card from a standard deck 5 times​ (replacing the card each time you​ draw, so there are always 52 cards in the​ deck)
drawing at least one queen is the opposite of drawing 5 times with no queen.
Since P(no queen) = 12/13, drawing no queen 5 times in a row is (12/13)^5
So, the chance of drawing at least one queen in 5 draws is 1-(12/13)^5 = 0.3298
Ah, drawing cards from a deck, a classic game of chance. Let's see if we can find some humor in math!
To calculate the probability of drawing at least one queen when you draw a card from a standard deck 5 times, we can use the concept of complementary probability.
The probability of NOT drawing a queen in one draw is 48/52, because there are 48 non-queen cards out of the total 52 cards in the deck. Since we are replacing cards after each draw, the probability remains the same for each draw.
So, the probability of NOT drawing a queen in 5 draws is (48/52)^5. To find the probability of drawing at least one queen, we need to subtract this value from 1 (since it's the complementary probability).
Therefore, the probability of drawing at least one queen when you draw a card from a standard deck 5 times is 1 - (48/52)^5.
And remember, even if you don't draw a queen, there's always a chance for some royal laughter along the way!
To find the probability of drawing at least one queen when you draw a card from a standard deck 5 times, we can use the concept of complementary probability.
Step 1: Determine the probability of not drawing a queen in a single draw.
There are 52 cards in a standard deck, and 4 of them are queens. So, the probability of not drawing a queen in a single draw is:
P(not drawing a queen) = (Number of cards that are not queens) / (Total number of cards)
= (52 - 4) / 52
= 48 / 52
= 12 / 13
Step 2: Determine the probability of not drawing a queen in all 5 draws.
Since we are replacing the card after each draw, the probability of not drawing a queen in all 5 draws is:
P(not drawing a queen in all 5 draws) = (P(not drawing a queen))^5
= (12/13)^5
Step 3: Use complementary probability to find the probability of drawing at least one queen.
The probability of drawing at least one queen is equal to 1 minus the probability of not drawing a queen in all 5 draws:
P(drawing at least one queen) = 1 - P(not drawing a queen in all 5 draws)
= 1 - (12/13)^5
Therefore, the probability of drawing at least one queen when you draw a card from a standard deck 5 times is 1 - (12/13)^5, or approximately 0.4115 (41.15%).
To find the probability of drawing at least one queen when you draw a card from a standard deck 5 times, you need to consider the total number of favorable outcomes and the total number of possible outcomes.
Total number of possible outcomes:
Since there are 52 cards in a standard deck and you draw a card 5 times (replacing the card each time), the total number of possible outcomes is 52^5.
Total number of favorable outcomes:
To calculate the number of favorable outcomes, we need to consider the complementary event, which is drawing no queens in 5 draws.
Number of favorable outcomes (drawing no queens):
For each draw, there are 48 cards that are not queens out of the 52 cards in the deck. Therefore, the probability of drawing a non-queen in one draw is 48/52. Since we replace the card after each draw, the probability remains the same for each draw. Hence, the probability of drawing no queens in all 5 draws is (48/52)^5.
Number of favorable outcomes (drawing at least one queen):
The complementary event of drawing no queens is drawing at least one queen. So, the number of favorable outcomes is the complement of drawing no queens in 5 draws. Thus, the number of favorable outcomes is 52^5 - (48/52)^5.
Probability of drawing at least one queen:
To get the probability, divide the number of favorable outcomes (drawing at least one queen) by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (52^5 - (48/52)^5) / 52^5
Calculating this value will give you the probability of drawing at least one queen when you draw a card from a standard deck 5 times.