The table shows how many players won a prize at the dart throw game and duck pond game during a day at a festival. Find the probability that a player won a prize given that he or she played the duck pond game. Prizes won at dart throw 44, 236 no prize - duck pond prize 41, 205 no prize
No table. Stats unclear. Cannot copy and paste here.
To find the probability that a player won a prize given that they played the duck pond game, we need to calculate the conditional probability.
Conditional probability is computed using the formula:
P(A|B) = P(A ∩ B) / P(B)
Where:
- P(A|B) is the probability of event A occurring given that event B has already occurred.
- P(A ∩ B) is the probability of both A and B occurring.
- P(B) is the probability of event B occurring.
In this case, event A is winning a prize and event B is playing the duck pond game.
From the given table, we know:
- Prizes won at the dart throw game = 44
- No prize won at the dart throw game = 236
- Prizes won at the duck pond game = 41
- No prize won at the duck pond game = 205
To find P(A ∩ B) (the probability of winning a prize and playing the duck pond game), we need to know how many players won a prize at both the dart throw game and the duck pond game. However, this information is not provided in the table. Without this information, we cannot directly calculate P(A ∩ B).
Hence, we cannot determine the exact value of the conditional probability without additional data.