In a game, a golf ball is putted into a tunnel. When it exits the tunnel, it randomly comes to rest in a square area which has been divided into a number of equal sections. Tokens have been placed in some of these sections. If the golf ball comes to rest in one of the sections with a token, the player wins. Janice and Lara played the game a number of times and recorded their wins and losses in the table shown. Part a) Use the table to calculate two different estimates for the probability of winning the game.
We can find the probability of an event occurring by dividing the number of ways that event can occur by the total number of outcomes. In this example, to find the probability of winning, that’s our event, we need to find the number of wins and we need to divide it by the total number of games played. There are actually three different ways of finding this probability. The first is to consider Janice’s results. The second is to consider Lara’s results. And the third way of finding that probability is to find the total of Janice and Lara’s results combined.
Let’s begin by calculating the total number of times that Janice played the game. She won the game 11 times and she lost 35 times. In total, 11 plus 35 is 46. So Janice played the game 46 times. Lara won the game 24 times and lost it 81 times. 24 plus 81 is 105. So that means Lara played the game 105 times. We can use Janice’s results to find one estimate for the probability of winning the game. She won 11 times, and she played a total of 46 games. So according to her results, the probability of winning is 11 over 46.
Alternatively, we could use Lara’s results. She won the game 24 times out of a total of 105 games. So the probability of winning according to her results is 24 over 105. This is sufficient to answer the question. But we did say there was one more estimate we could use, we said there was a third way to calculate the probabilities, and that’s to look at the total of their results combined. 11 plus 24 is 35 and 46 plus 105 is 151. We can use this combination of results to find an estimate for the probability of winning the game; it’s 35 over 151. Any two of these three probabilities will be sufficient to answer this question.
Part b) Determine which of your probabilities is a better estimate for the probability of winning. You must give a reason for your answer. We have been working with experimental probability. We’re finding probabilities based on experiments. With experimental probability, the more trials we do, the more accurate our results will be. The answer to this question will very much depend on what you wrote for part a. If you included the probability of winning as being 35 over 151, then this will be the most accurate probability. And that’s because it’s based on the most results. It’s based on 151 games. It may be though that you just use Lara’s and Janice’s results. In this case, you would say that Lara’s results are more accurate. She played the game 105 times, whereas Janice only played it 46 times.