"Golf Balls
The local golf store sells an “onion bag” that contains 35 “experienced” golf balls. Suppose that the bag contains 20 Titleists, 8 Maxflis, and 7 Top Flites. Use a tree diagram like the one in Example 5 to answer the following:


b. What is the probability that the first ball selected is a Titleist and the second is a Maxfli?"

Verified step by step guidance

1. Identify the total number of golf balls in the bag. Since the bag contains 20 Titleists, 8 Maxflis, and 7 Top Flites, calculate the total as \$20 + 8 + 7$.
2. Determine the probability of selecting a Titleist on the first draw. This is the number of Titleists divided by the total number of balls, expressed as \(\frac{20}{35}\).
3. After selecting one Titleist, update the total number of balls remaining. Since one ball is removed, the new total is \$35 - 1$.
4. Calculate the probability of selecting a Maxfli on the second draw, given that the first ball was a Titleist. The number of Maxflis remains the same (8), so the probability is \(\frac{8}{34}\).
5. Multiply the probabilities of the two independent events (first ball is Titleist and second ball is Maxfli) to find the combined probability: \(\frac{20}{35} \times \frac{8}{34}\).

Key Concepts

Probability of Sequential Events

This concept involves calculating the likelihood of two or more events happening in a specific order. When events occur one after another, the probability of the combined event is found by multiplying the probability of the first event by the probability of the second event, considering any changes in the sample space after the first event.

Tree Diagrams

A tree diagram is a visual tool used to map out all possible outcomes of a sequence of events. Each branch represents a possible outcome and its probability, helping to organize and calculate combined probabilities systematically, especially for dependent or sequential events.

Dependent Events

Dependent events are events where the outcome of the first affects the probability of the second. In this problem, selecting the first ball changes the total number of balls left, which alters the probability of selecting the second ball. Recognizing dependency is crucial for accurate probability calculation.