A reading list contains 3 historical books and 4 science-fiction books. What is the probability that Tena will randomly choose a historical book for her first report and a science-fiction book for her second?
To find the probability of Tena randomly choosing a historical book for her first report and a science-fiction book for her second report, we need to consider the total number of books and calculate the probability for each step.
Step 1: Calculating the probability of choosing a historical book for the first report.
Since there are 3 historical books out of a total of 7 books (3 historical + 4 science-fiction), the probability of choosing a historical book for the first report is 3/7.
Step 2: Calculating the probability of choosing a science-fiction book for the second report.
After Tena has chosen a historical book for her first report, there are now 2 historical books left and a total of 6 books remaining (including 3 historical and 3 science-fiction books). Therefore, the probability of choosing a science-fiction book for the second report is 3/6.
Step 3: Calculating the overall probability.
To find the overall probability, we multiply the probabilities from each step.
P(Choosing historical book for first report) × P(Choosing science-fiction book for second report)
= (3/7) × (3/6) = 9/42 = 3/14
Therefore, the probability that Tena will randomly choose a historical book for her first report and a science-fiction book for her second report is 3/14.