Chapter 53, Problem 2.1A

Single penny tossed 20 times and counting heads and tails:
Probability (prediction): _______/20 heads ________/20 tails
(Note: Traditionally, probabilities are converted to the lowest fractional representation.)
Actual results: ______heads ______tails
Class totals: ______heads ______tails

Summary Introduction

To analyze:

Single penny tossed 20 times and counting the heads and tails.

Introduction:

Probability__10__/20 heads__ 10_/20 tails

Actual rates _1___heads

Class result 19__tails.

Probability are written as number between zero and one.

Probability of one means that the event is certain.

Explanation of Solution

Tossing a coin 20 times can give 2 outcomes.

So, the probability of getting at least one head $=\left[\left\{\left(2\times 20\right)-1\right\}/\left(2\times 20\right)\right]=\left[1-\{1/\left(2\times 20\right)\}\right]$

.There will be exactly one case in which tails. no heads show up

Therefore, the probability of getting one head at least one heads is $\left(220-1/220\right)=1048575/1048576=0.9999990463$

The probability of single penny tossed of any one of them is $\left(1/2\right)20$

Probability 10 /20 heads 10/20tails so actual rates 1heads and class result 19 tails.

One head only out of 20 tossed. So class result will be 19 tails.

Conclusion

Single penny tossed 20 times and counting heads1and tails 19. So the probability of fraction is

10 /20 heads and 10 /20 tails are converted to the lowest fractional representation.