Revision as of 01:44, 20 June 2024 by Admin (Created page with "A coin is tossed twice. Consider the following events. <math>A</math>: Heads on the first toss. <math>B</math>: Heads on the second toss. <math>C</math>: The two tosses come out the same. Which one of the following statements is true? <ul style="list-style-type:lower-alpha"> <li><math>A</math>, <math>B</math>, <math>C</math> are independent. </li> <li> <math>C</math> is independent of <math>A</math> and <math>B</math> but not of <math>A \cap B</math>. </li> <li> <...")
Jun 20'24
Exercise
A coin is tossed twice. Consider the following events.
[math]A[/math]: Heads on the first toss.
[math]B[/math]: Heads on the second toss.
[math]C[/math]: The two tosses come out the same.
Which one of the following statements is true?
- [math]A[/math], [math]B[/math], [math]C[/math] are independent.
- [math]C[/math] is independent of [math]A[/math] and [math]B[/math] but not of [math]A \cap B[/math].
- [math]C[/math] is mutually independent from [math]A[/math] but not of [math]B[/math].
- [math]C[/math] is mutually independent from [math]B[/math] and mutually independent of [math]A \cap B[/math].
- [math]C[/math] is independent of [math]A-B[/math] and also independent of [math]B-A[/math].
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.