martinezadam576
Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Select the correct answer.

Two events, [tex]E_1[/tex] and [tex]E_2[/tex], are defined for a random experiment. What is the probability that at least one of the two events occurs in any trial of the experiment?

A. [tex]P(E_1) - P(E_2) - P(E_1 \cap E_2)[/tex]

B. [tex]P(E_1) + P(E_2) - P(E_1 \cap E_2)[/tex]

C. [tex]P(E_1) + P(E_2) + P(E_1 \cap E_2)[/tex]

D. [tex]P(E_1) + P(E_2) - 2 P(E_1 \cap E_2)[/tex]

Sagot :

GinnyAnswer
To find the probability that at least one of the two events [tex]\(E_1\)[/tex] and [tex]\(E_2\)[/tex] occurs in any trial of the experiment, we need to use the formula for the union of two probabilities. The correct formula for the probability that at least one of two events occurs is given by:

[tex]\[ P(E_1 \cup E_2) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \][/tex]

This formula accounts for the fact that when you add the probabilities of [tex]\(E_1\)[/tex] and [tex]\(E_2\)[/tex], the intersection (where both events happen) is counted twice. Therefore, you subtract the intersection once to get the correct probability of at least one event occurring.

Given this information, we can determine that the correct answer is:

[tex]\[ \boxed{B. \ P(E_1) + P(E_2) - P(E_1 \cap E_2)} \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.