Questions: Determine whether the following individual events are overlapping or non-overlapping. Then find the probability of the combined event.
Drawing either a black two or a red three on one draw from a regular deck of cards
Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
(Type an integer or a simplified fraction.)
A. The individual events are non-overlapping. The probability of the combined event is .
B. The individual events are overlapping. The probability of the combined event is
Transcript text: Determine whether the following individual events are overlapping or non-overlapping. Then find the probability of the combined event.
Drawing either a black two or a red three on one draw from a regular deck of cards
Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
(Type an integer or a simplified fraction.)
A. The individual events are non-overlapping. The probability of the combined event is $\square$ .
B. The individual events are overlapping. The probability of the combined event is $\square$
Solution
Solution Steps
Step 1: Determine Overlap
Given that Event A (black two) and Event B (red three) are non-overlapping, based on the overlap condition: False.
Step 2: Calculate Combined Probability
Since the events are non-overlapping, we use the formula $P(A \cup B) = P(A) + P(B)$ to calculate the combined probability.
Substituting the given probabilities, $P(A \cup B) = 0.0385 + 0.0769 = 0.12$.
Final Answer:
The probability of either Event A (black two) or Event B (red three) occurring is 0.12.