Maya answers three quiz questions in a row…

Step 1. The tree. Write R for right and W for wrong. The branches are in the picture, with the probability of each step given the earlier answer.

Step 2. All three right. RRR: $0.8 \times 0.9 \times 0.9 = 0.648$.

Step 3. Exactly two right. RRW: $0.8 \times 0.9 \times 0.1 = 0.072$. RWR: $0.8 \times 0.1 \times 0.5 = 0.04$. WRR: $0.2 \times 0.5 \times 0.9 = 0.09$. The sum is $0.072 + 0.04 + 0.09 = 0.202$.

Step 4. At least one right. The only way to get none is WWW: $0.2 \times 0.5 \times 0.5 = 0.05$. So the answer is $1 - 0.05 = 0.95$.