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A penny is tossed three times and the results heads and tails noted. The process is continued until there are 100 sets of threes. In 69 cases, heads fell first, in 49 cases, heads fell second and in 53 cases. Heads fell third. In 33 cases heads fell both first and second and in 21 cases heads fell both second and third. Show that there must have been at least 5 occasions on which heads fell three times, and that there could not have been more than 15 occasions on which tails fell three times, though there need not have been any.

A penny is tossed three times and the results heads and tails noted. The process is continued until there are 100 sets of threes. In 69 cases, heads fell first, in 49 cases, heads fell second and in 53 cases. Heads fell third. In 33 cases heads fell both first and second and in 21 cases heads fell both second and third. Show that there must have been at least 5 occasions on which heads fell three times, and that there could not have been more than 15 occasions on which tails fell three times, though there need not have been any.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A penny is tossed three times and the results heads and tails noted. The process is continued until there are 100 sets of threes. In 69 cases, heads fell first, in 49 cases, heads fell second and in 53 cases. Heads fell third. In 33 cases heads fell both first and second and in 21 cases heads fell both second and third. Show that there must have been at least 5 occasions on which heads fell three times, and that there could not have been more than 15 occasions on which tails fell three times, though there need not have been any.
Transcribed Image Text:A penny is tossed three times and the results heads and tails noted. The process is continued until there are 100 sets of threes. In 69 cases, heads fell first, in 49 cases, heads fell second and in 53 cases. Heads fell third. In 33 cases heads fell both first and second and in 21 cases heads fell both second and third. Show that there must have been at least 5 occasions on which heads fell three times, and that there could not have been more than 15 occasions on which tails fell three times, though there need not have been any.
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