what is the probability of drawing at least one five when you draw a card from a standard deck 7 times (replacing the card each time you draw)
To calculate the probability of drawing at least one five when you draw a card from a standard deck 7 times with replacement, we can use the concept of complementary probability.
First, let's calculate the probability of not drawing a five in one draw. In a standard deck, there are 52 cards, and 4 of them are fives. So, the probability of not drawing a five in one draw is 48/52.
Since we are drawing with replacement, the probability of not drawing a five in any of the 7 draws is (48/52) multiplied by itself 7 times. So, the probability of not drawing a five in 7 draws is:
(48/52)^7 ≈ 0.4745 (rounded to four decimal places)
Now we can calculate the probability of drawing at least one five by subtracting the probability of not drawing a five from 1:
1 - 0.4745 = 0.5255 (rounded to four decimal places)
The probability of drawing at least one five when drawing a card from a standard deck 7 times with replacement is approximately 0.5255, or 52.55%.