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.