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Two fair coins are tossed, and the following events are
Chapter 3, Problem 54E(choose chapter or problem)
Problem 54E
Two fair coins are tossed, and the following events are defined: A: {Observe at least one head} B: {Observe exactly one head}
a. Draw a Venn diagram for the experiment, showing events A and B. Assign probabilities to the sample points.
b. Find P(A), P(B), and P(A B)
c. Use the formula for conditional probability to find P(A|B) and P(B|A). Verify your answer by inspecting the Venn diagram and using the concept of reduced sample spaces.
Questions & Answers
QUESTION:
Problem 54E
Two fair coins are tossed, and the following events are defined: A: {Observe at least one head} B: {Observe exactly one head}
a. Draw a Venn diagram for the experiment, showing events A and B. Assign probabilities to the sample points.
b. Find P(A), P(B), and P(A B)
c. Use the formula for conditional probability to find P(A|B) and P(B|A). Verify your answer by inspecting the Venn diagram and using the concept of reduced sample spaces.
ANSWER:
Solution:
Step 1 of 4:
It is given that the experiment under consideration is tossing two fair coins.
Event A is defined as getting atleast one head and event B is defined as getting exactly one head.
Using this we need to find the required values.