Question: If two events A and B are independent, what is the probability of both A and B occurring?
Options:
P(A) + P(B)
P(A) * P(B)
P(A) - P(B)
P(A) / P(B)
Correct Answer: P(A) * P(B)
Solution:
For independent events, P(A and B) = P(A) * P(B).
If two events A and B are independent, what is the probability of both A and B o
Practice Questions
Q1
If two events A and B are independent, what is the probability of both A and B occurring?
P(A) + P(B)
P(A) * P(B)
P(A) - P(B)
P(A) / P(B)
Questions & Step-by-Step Solutions
If two events A and B are independent, what is the probability of both A and B occurring?
Step 1: Understand what independent events are. Independent events are events that do not affect each other. This means the occurrence of one event does not change the probability of the other event occurring.
Step 2: Identify the probabilities of each event. Let's say the probability of event A occurring is P(A) and the probability of event B occurring is P(B).
Step 3: Use the formula for independent events. For independent events, the probability of both A and B occurring together is found by multiplying their individual probabilities.
Step 4: Write the formula. The formula is P(A and B) = P(A) * P(B). This means you take the probability of A and multiply it by the probability of B to find the probability of both happening.
Independence of Events – Two events A and B are independent if the occurrence of one does not affect the occurrence of the other.
Probability of Joint Events – The probability of both independent events A and B occurring is calculated by multiplying their individual probabilities.
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