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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> You are given two urns each containing two biased coins. The coins in urn I come up heads with probability <math>p_1</math>, and the coins in urn II come up heads with probability <math>p_2 \ne p_1</math>. You are given a choice of (a) choosing...") |
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You are given two urns each containing two biased coins. The coins in urn I come up heads with probability <math>p_1</math>, and the coins in urn II come up heads with probability <math>p_2 \ne p_1</math>. You are given a choice of (a) choosing | |||
urn I come up heads with probability <math>p_1</math>, and the coins in urn II come up | |||
heads with probability <math>p_2 \ne p_1</math>. You are given a choice of (a) choosing | |||
an urn at random and tossing the two coins in this urn or (b) choosing one coin | an urn at random and tossing the two coins in this urn or (b) choosing one coin | ||
from each urn and tossing these two coins. You win a prize if both coins turn | from each urn and tossing these two coins. You win a prize if both coins turn | ||
up heads. Show that you are better off selecting choice (a). | up heads. Show that you are better off selecting choice (a). | ||
Latest revision as of 01:12, 13 June 2024
You are given two urns each containing two biased coins. The coins in urn I come up heads with probability [math]p_1[/math], and the coins in urn II come up heads with probability [math]p_2 \ne p_1[/math]. You are given a choice of (a) choosing an urn at random and tossing the two coins in this urn or (b) choosing one coin from each urn and tossing these two coins. You win a prize if both coins turn up heads. Show that you are better off selecting choice (a).