The probability of drawing a heart from a standard deck of cards is 0.25 . You record the card you draw and return the card before shuffling to ensure a binomial distribution. If you do this 20 times, what is the probability that you will draw a heart 7 times? (1 point) 0.888 0.001 0.412

To calculate the probability of drawing a heart exactly 7 times in 20 trials from a standard deck of cards, we can use the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success on each trial. Here, n = 20, k = 7, and p = 0.25. Substituting in the values: P(X = 7) = (20 choose 7) * (0.25^7) * (0.75^(20-7)). Calculating this and approximating, you'll find that the probability of drawing a heart exactly 7 times is approximately 0.001. So, the correct answer is 0.001! Doesn’t mathematics mix a little thrill with probability? Just think about how many times you could end up with those ruby-red hearts! It’s a classic card game moment, right? And if you ever find yourself perplexed surrounded by cards, just remember, every shuffle gives you another chance!