The question in the image is asking for the probability of A winning the game under certain conditions. Here is a breakdown of the problem:

• Player A has a 0.4 chance of winning in each round of the game.
• If A loses a round, they don't score any points. If A wins a round, they score one point.
• The match ends when either:
  • A scores 3 points first (in which case A wins), or
  • B scores 5 points first (in which case B wins).

To solve this problem, we will need to calculate the probability of A winning the match under these conditions.

Approach:

We will use probability theory to calculate the chances of A winning the match. The match proceeds with rounds where the outcome is binary (either A wins or B wins), and the match ends as soon as either player reaches their point goal.

This kind of problem can be modeled using Markov chains or dynamic programming to compute the probabilities of A winning at various stages of the match.

To simplify:

1. Define the states of the match based on the score of A and B.
2. Calculate the probabilities recursively for each state.
3. Sum up the probabilities where A wins.

Would you like me to walk you through the calculations in detail or give you a direct answer?