Contestants on a gameshow spin a wheel with 24 equally-sized segments. Most of thos...
Check the final answer first, then review the worked steps.
Answer
The probability that the first spin lands on bankrupt AND the second spin lands on bankrupt.
Step-by-step solution
- Understand the notation: The problem defines events $B_1$ and $B_2$. $B_1$ represents the event that the first spin lands on bankrupt. $B_2$ represents the event that the second spin lands on bankrupt. The notation $P(B_1 \text{ and } B_2)$ represents the probability that both event $B_1$ and event $B_2$ occur.
- Interpret the given formula: The formula provided is $P(B_1 \text{ and } B_2) = P(B_1) \cdot P(B_2 \mid B_1)$. This is the general multiplication rule for probabilities, which states that the probability of two events occurring is the probability of the first event multiplied by the conditional probability of the second event given that the first event has occurred.
- Apply the formula to the context: In this specific context, $P(B_1)$ is the probability that the first spin lands on bankrupt. $P(B_2 \mid B_1)$ is the probability that the second spin lands on bankrupt, given that the first spin already landed on bankrupt. Therefore, their product, $P(B_1 \text{ and } B_2)$, represents the probability that the first spin lands on bankrupt AND the second spin also lands on bankrupt.