Probability: Which of the following three outcomes has the greatest chance of occuring?

Which of the following three outcomes has the greatest chance of occuring? (Assuming normal six-sided fair dice)

- throwing a die 6 times and getting at least one 6? (i.e. one or more sixes)

- throwing a die 12 times and getting at least two sixes ?

- throwing a die 18 times and getting at least three sixes ?Good question.

The probability of NOT getting what you want in 6 throws is

(5/6)^6 = 0.3348979767

The probability of NOT getting what you want in 12 throws is

(5/6)^12 + 12[(5/6)^11]/6

The first term in the above expression is the probability of getting zero 6's in 12 throws. The second term is the probability of getting exactly one 6. The multiplication by 12 in the second term is because there are 12 equally likely ways that exactly one 6 in 12 throws can come up.

= 0.11215665477 + 12*0.13458798573/6

= 0.11215665477 + 0.26917597142

= 0.3813326262

This is the probability of getting less than two 6's in 12 throws.

In general, as the number of trials increases, the probability of getting LESS than the expected proportion of 6's (1/6) also tends to increase. In this particular problem, your likelihood of success is better with 6 throws than with 12 or 18 throws.

Related Discussions

- 5
### A coin is tossed on 5 occasions .What is the probability that a head will appear

by tqr0078 years ago

A coin is tossed on 5 occasions .What is the probability that a head will appear on all 5 occasions

- 16
### probability

by seanorjohn8 years ago

This is trickier than it looks and has caught out people with higher degrees in maths.Three playing cards are shuffled (one ace and two kings). The ace is the winning card.Someone is asked to select a card but not to...

Copyright © 2018 HubPages Inc. and respective owners.

Other product and company names shown may be trademarks of their respective owners.

HubPages^{®} is a registered Service Mark of HubPages, Inc.

HubPages and Hubbers (authors) may earn revenue on this page based on affiliate relationships and advertisements with partners including Amazon, Google, and others.

terms of use privacy policy (0.41 sec)

working