1. **Problem statement:** Calculate the probabilities of drawing sequences of red (R) and blue (B) balls from a set where the probability of red is $0.6$ and blue is $0.4$, following the given tree diagram. 2. **Given:** - $P(\text{red}) = 0.6$ - $P(\text{blue}) = 0.4$ 3. **Understanding the tree diagram:** - First draw: red with probability $0.6$, blue with probability $0.4$. - Second draw depends on the first: - If first is red, second is red with $0.6$, blue with $0.4$. - If first is blue, second is red with $0.6$, blue with $0.4$. 4. **Calculate probabilities for each two-draw sequence:** - $P(RR) = P(R) \times P(R|R) = 0.6 \times 0.6 = 0.36$ - $P(RB) = P(R) \times P(B|R) = 0.6 \times 0.4 = 0.24$ - $P(BR) = P(B) \times P(R|B) = 0.4 \times 0.6 = 0.24$ - $P(BB) = P(B) \times P(B|B) = 0.4 \times 0.4 = 0.16$ 5. **Check total probability:** $$0.36 + 0.24 + 0.24 + 0.16 = 1.0$$ 6. **Interpretation:** - The probabilities of all possible two-draw sequences sum to 1, confirming the correctness. **Final answer:** - $P(RR) = 0.36$ - $P(RB) = 0.24$ - $P(BR) = 0.24$ - $P(BB) = 0.16$