A bowl is filled with 5 red, 6 yellow, and 4 white balls. What is the probability of drawing a red ball and then a white ball at random?

To solve this problem, we first need to determine the total number of balls in the bowl, which is 5 red + 6 yellow + 4 white = 15 balls in total. The probability of drawing a red ball first is the number of red balls (5) divided by the total number of balls (15), giving us a probability of 5/15 or 1/3. Once we successfully draw a red ball, the total number of balls left in the bowl is 14 (since we took one red ball out). There are still 4 white balls remaining. The probability of then drawing a white ball is 4/14, which simplifies to 2/7. To find the combined probability of both events happening (drawing a red ball first and then a white ball), we multiply the two probabilities: (1/3) * (2/7) = 2/21. Thus, the probability of drawing a red ball and then a white ball is 2/21. If you’re pondering probabilities in day-to-day life, think of games! Whether it's playing poker or guessing the right candy from a jar, knowing how to calculate probabilities helps sharpen your skills and enhance your strategies. For an amusing twist, in 1756, the British mathematician Thomas Bayes introduced the concept of probability as a measure of uncertainty. His work laid the foundations of modern probability theory, and just like choosing balls from a bowl, it helps mathematicians and gamblers alike make sense of chance. So, next time you roll the dice or draw a card, you can thank Bayes for his pivotal contribution!