exercise:0990624caa: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> A coin is tossed three times. Consider the following events\newline <math>A</math>: Heads on the first toss.\newline <math>B</math>: Tails on the second.\newline <math>C</math>: Heads on the third toss.\newline <math>D</math>: All three outcomes...") |
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A coin is tossed three times. Consider the following events | |||
<math>A</math>: Heads on the first toss. | |||
<math>B</math>: Tails on the second. | |||
<math>C</math>: Heads on the third toss. | |||
<math>A</math>: Heads on the first toss. | |||
<math>B</math>: Tails on the second. | <math>D</math>: All three outcomes the same (HHH or TTT). | ||
<math>C</math>: Heads on the third toss. | |||
<math>D</math>: All three outcomes the same (HHH or TTT). | |||
<math>E</math>: Exactly one head turns up. | <math>E</math>: Exactly one head turns up. | ||
<ul><li> Which of the following pairs of these events are independent? | <ul style="list-style-type:lower-alpha"><li> Which of the following pairs of these events are independent? | ||
(1) <math>A</math>, <math>B</math> | |||
(2) <math>A</math>, <math>D</math> | (1) <math>A</math>, <math>B</math> | ||
(3) <math>A</math>, <math>E</math> | |||
(2) <math>A</math>, <math>D</math> | |||
(3) <math>A</math>, <math>E</math> | |||
(4) <math>D</math>, <math>E</math> | (4) <math>D</math>, <math>E</math> | ||
</li> | </li> | ||
<li> Which of the following triples of these events are | <li> Which of the following triples of these events are | ||
independent? | independent? | ||
(1) <math>A</math>, <math>B</math>, <math>C</math> | |||
(2) <math>A</math>, <math>B</math>, <math>D</math> | (1) <math>A</math>, <math>B</math>, <math>C</math> | ||
(2) <math>A</math>, <math>B</math>, <math>D</math> | |||
(3) <math>C</math>, <math>D</math>, <math>E</math> | (3) <math>C</math>, <math>D</math>, <math>E</math> | ||
</li> | </li> | ||
</ul> | </ul> | ||
Latest revision as of 23:40, 12 June 2024
A coin is tossed three times. Consider the following events
[math]A[/math]: Heads on the first toss.
[math]B[/math]: Tails on the second.
[math]C[/math]: Heads on the third toss.
[math]D[/math]: All three outcomes the same (HHH or TTT).
[math]E[/math]: Exactly one head turns up.
- Which of the following pairs of these events are independent? (1) [math]A[/math], [math]B[/math] (2) [math]A[/math], [math]D[/math] (3) [math]A[/math], [math]E[/math] (4) [math]D[/math], [math]E[/math]
- Which of the following triples of these events are independent? (1) [math]A[/math], [math]B[/math], [math]C[/math] (2) [math]A[/math], [math]B[/math], [math]D[/math] (3) [math]C[/math], [math]D[/math], [math]E[/math]