A box contained 6 red and 4 blue crayons. Fir probability that the first crayon is blue and the A \( \frac{6}{25} \) B \( \frac{18}{45} \) C \( \frac{4}{15} \) D \( \frac{3}{4} \)

The probability of drawing a blue crayon first is calculated by dividing the number of blue crayons by the total number of crayons. So, that would be \( P(\text{Blue}) = \frac{4}{10} = \frac{2}{5} \). Now, if the first crayon drawn is blue, there are still 6 red and 3 blue crayons remaining, making the total crayons now 9. The probability of drawing a red crayon next would be \( P(\text{Red | Blue}) = \frac{6}{9} = \frac{2}{3} \). So, the combined probability of first drawing a blue crayon and then a red crayon can be calculated as follows: \( P(\text{Blue first, then Red}) = \frac{4}{10} \times \frac{6}{9} = \frac{24}{90} = \frac{4}{15} \). Therefore, the correct answer is C \( \frac{4}{15} \). In case you were wondering, there are clever ways to make sure your calculations are spot on. Always write down the total number of items you have at each step and the number remaining after each draw – it’s a lifesaver for keeping track of everything. And remember, practicing with different combinations will sharpen your skills and make those probability calculations feel like second nature! Further exploration into probability topics, like Bayes' theorem, can be quite rewarding. You might consider checking out a probability textbook or online resources that dive deeper into concepts such as conditional probability and events. It’s a fascinating field that pops up in everything from games to statistical analysis in scientific research!