2025 TJC P2 Q5

In a simple archery game, a player shoots an arrow at a target. The probability of hitting the target depends on the player’s skill and the wind conditions for the day. The wind can either be good or bad, with the probability of a good wind day being \(0.7\).

According to past statistics:

• Dave has a \(70\)% chance of hitting the target on a good wind day and a \(60\)% chance on a bad wind day.
• Rafael has an \(80\)% chance of hitting the target on a good wind day and a \(50\)% chance on a bad wind day.

Dave and Rafael decide to compete in a game where each player shoots \(2\) arrows at the target. The player who hits the target more times wins the game.

1. Find the probability that Dave wins the game on a good wind day.[3]

It is now known that the probability Dave wins the game on a bad wind day is \(0.39\).

2. Given that Dave wins the game, find the probability that the day was a bad wind day.[3]