Bowling
Suppose that Ralph gets a strike when bowling 30% of the time.


c. When events are independent, their complements are independent as well. Use this result to determine the probability that Ralph gets a turkey, but fails to get a clover (four strikes in a row).

Verified step by step guidance

1. Identify the probability of Ralph getting a strike, which is given as \(P(\text{strike}) = 0.30\).
2. Understand that a 'turkey' in bowling means getting three strikes in a row, so calculate the probability of three consecutive strikes as \(P(\text{turkey}) = P(\text{strike})^3 = (0.30)^3\).
3. Recognize that a 'clover' means four strikes in a row, so the probability of a clover is \(P(\text{clover}) = P(\text{strike})^4 = (0.30)^4\).
4. Since events are independent, the complement of getting a clover (not getting four strikes in a row) is \(P(\text{not clover}) = 1 - P(\text{clover})\).
5. To find the probability that Ralph gets a turkey but fails to get a clover, multiply the probability of a turkey by the probability of not getting a clover: \(P(\text{turkey and not clover}) = P(\text{turkey}) \times P(\text{not clover})\).

Key Concepts

Independence of Events

Two events are independent if the occurrence of one does not affect the probability of the other. This means the probability of both events happening together is the product of their individual probabilities. Understanding independence is crucial for calculating combined probabilities in sequences of events.

Complement of an Event

The complement of an event is the outcome where the event does not occur. The probability of the complement is 1 minus the probability of the event. Knowing how to use complements helps simplify probability calculations, especially when dealing with 'not' scenarios.

Probability of Consecutive Events (Strikes in a Row)

When events are independent, the probability of multiple consecutive occurrences is the product of their individual probabilities. For example, the probability of getting four strikes in a row is the strike probability raised to the fourth power. This concept is key to solving problems involving sequences like a turkey or clover in bowling.