Probability problems involving coins and letters.

[megadeth95]

Hello guys, I need some help with the following problems:

1. A coin is tossed 6 times. Find the probability that you get all heads.
2. If you have 1 M, 4 I's, 4 S's, and 2 P's, find the probability that all the letters spell MISSISSIPPI.
3. If there are 8 married (man/woman) couples in a club and one man and one woman is selected at random to plan a tournament, find the probability that they are married to each other.

Thanks in advance

 

[soroban]

Hello, megadeth95!

A coin is tossed 6 times. .Find the probability that you get all Heads.

There are: .\(\displaystyle 2^6 = 64\) possible outomes.

Only one outcome has all Heads.

Therefore: .\(\displaystyle P(\text{all Heads}) \:=\:\dfrac{1}{64}\)

If you have 1 M, 4 I's, 4 S's, and 2 P's,
find the probability that all the letters spell MISSISSIPPI.

There are: .\(\displaystyle \dfrac{11!}{1!\,4!\,4!\,2!} \:=\:34,\!650\) possible orderings of the letters.

There is one ordering which spells MISSISSIPPI.

Therefore: .\(\displaystyle P(\text{MISSISSIPPI}) \:=\:\dfrac{1}{34,\!650}\)

If there are 8 married (man/woman) couples in a club
and one man and one woman is selected at random to plan a tournament,
find the probability that they are married to each other.

One man is chosen . . . It doesn't matter which man.

Then one woman is chosen.
The probability that the woman is the chosen man's wife is \(\displaystyle \frac{1}{8}\)

Therefore: .\(\displaystyle P(\text{married couple chosen}) \:=\:\dfrac{1}{8}\)

 

[megadeth95]

Thank you very much soroban, I really appreciate your help!!