Hello everyone, i'm having some issues on this problem:(adsbygoogle = window.adsbygoogle || []).push({});

A coin is tossed ten times. In each case the outcome H (for heads) or T (for tails) is recorded. (One possible outcome of the ten tossings is denoted THHTTTHTTH.)

I got a, d right i believe.

but I need someone to check if i did the others ones right.

a. what is the total number of possible outcomes of the coin-tossing experiemnt?

I said: 2^10 = 1,024

b. In how many of the possible outcomes are exactly 5 heads obtained?

[# of outcomes with exactly 5 heads] = [total # of outcomes] - (10 choose 5)

This one I'm not sure what i'm suppose to do, when i say 10 choose 5, i mean you have a set of 10, and i'm wanting to choose 5 elements out of that set that are H but i'm not sure how to represeent this...

c. In how many of the possible outcomes is at least 8 heads obtained?

For this one would i do:

[# of outcomes with at least 8 heads obtained] = [total number of outcomes] - [number of outcomes that contain 8 heads]

= 1024 - (10 choose 8)

= 1024 - 10!/[8!(2!)]

= 1024 - 45 = 979

d. In how many of the possible outcomes is at least one head obtained?

[# of outcomes w/ at least 1 head] = [total # of outcomes] - [# of outcomes with no heads] = 1024 - 1 = 1023.

e. In how many of the possible outcomes is at most one head obtained?

I think i got this one, but the # of outcomes with 1 head i might have got wrong.

[# of outcomes with at most 1 head] = [# of outcomes with no heads] + [# outcomes with 1 head]

= 1 + (10 choose 1)

= 1 + 10!/[1!(10-1)!]

= 1 + 10!/9! = 11

Any help would be great, i'm having issues figuring out how to choose once i figure out the method it seems.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Counting problem, exactly 5 heads obtained, coin

Loading...

Similar Threads for Counting problem exactly | Date |
---|---|

B Problem in Counting - Number of Passwords | Feb 23, 2018 |

Solving a counting problem | Nov 19, 2014 |

Problem Involving Counting of Elements in Three Sets | Oct 9, 2012 |

Counting problem (aabbcccdddd) | Apr 1, 2005 |

Counting Problems | Oct 21, 2004 |

**Physics Forums - The Fusion of Science and Community**