Bowling
Suppose that Ralph gets a strike when bowling 30% of the time.
a. What is the probability that Ralph gets two strikes in a row?

Verified step by step guidance

1. Identify the probability of Ralph getting a strike in a single attempt, which is given as 30%, or 0.30.
2. Understand that the problem asks for the probability of two strikes in a row, which means two independent events both resulting in strikes.
3. Recall that for independent events, the probability of both events occurring is the product of their individual probabilities.
4. Set up the multiplication of the probabilities: \(P(\text{two strikes in a row}) = P(\text{strike}) \times P(\text{strike})\).
5. Substitute the known probability into the formula: \(P(\text{two strikes in a row}) = 0.30 \times 0.30\).

Key Concepts

Probability of Independent Events

When two events are independent, the outcome of one does not affect the other. The probability of both events occurring together is the product of their individual probabilities. For example, if Ralph’s chance of a strike is 0.3 each time, the chance of two strikes in a row is 0.3 × 0.3.

Multiplication Rule for Probability

The multiplication rule states that to find the probability of multiple independent events all happening, multiply their probabilities. This rule applies directly to sequences like consecutive strikes in bowling, where each event’s probability is known and independent.

Understanding Probability Values

Probability values range from 0 to 1, where 0 means impossible and 1 means certain. A probability of 0.3 means there is a 30% chance of the event occurring. Interpreting these values helps in calculating and understanding the likelihood of combined events.