1. A bag contains six blue and seven red blocks. What is the probability of getting three blue block: four blocks are randomly selected?

To determine the probability of selecting three blue blocks when four blocks are randomly selected from a bag containing six blue and seven red blocks, we can use the hypergeometric distribution. The total number of blocks is 13 (6 blue + 7 red). The number of ways to choose 3 blue blocks from 6 is given by combinations, specifically \(\binom{6}{3}\), and to choose 1 red block from 7 is \(\binom{7}{1}\). The total ways to select 4 blocks from 13 is \(\binom{13}{4}\). Using this, the probability can be calculated by multiplying the combinations for the blue and red blocks, then dividing by the total combinations. The calculations yield: - Ways to choose 3 blue: \(\binom{6}{3} = 20\) - Ways to choose 1 red: \(\binom{7}{1} = 7\) - Total ways to choose 4 blocks: \(\binom{13}{4} = 715\) Thus, the probability \(P\) is \(P = \frac{20 \times 7}{715} = \frac{140}{715} \approx 0.196\) or about 19.6%. Now that's a colorful way to play with probabilities!