Trevor tosses a coin 3 times. Consider the following events.[br][math]A[/math]: The first toss is heads.[br][math]B[/math]: The second toss is heads.[br][math]C[/math]: There are exactly 2 consecutive heads.[br]For each of the following pairs of events, determine if the events are independent.[br][list][br][*][math]A[/math] and [math]B[/math] (This is [math]A∩B[/math] in set notation.)[br][*][math]A[/math] and [math]C[/math] (This is [math]A∩C[/math] in set notation.)[br][*][math]B[/math] and [math]C[/math] (This is [math]B∩C[/math] in set notation.)[br][/list]

[list=1][br][*]List the sample space.[br][*]Use the sample space to determine the relevant probabilities.[br][*]Use the definition of independence to determine if the events are independent in each specified pair.[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com]www.walch.com[/url] for more information.