How do I calculate the probability that atleast one will be tails when two coins or more are tossed?

Question

Lets say 0 Is Heads and 1 Is tails

If I toss a coin, there is 50% chances it lands on either side.
0
1

With two coins it means I could either have either
Option 1:

0 0
0 0
0 1
1 0
1 1
1 1

Or Option 2:

0 0
0 1
1 0
1 1

Option 1 of calculating it would mean my odds are 66.666666% chance to get at least one tails
Option 2 of calculating it would mean my odds are 75% chance to get at least one tails.

How do I calculate the probability that at least one will be tails when two coins or more are tossed?

And how to I calculate with elements that have 25% probabilities say two four 4 sided dice To know what is the odds to have atleast one, one

Answer 1

Ji-Kyung,

 

Probability is computed using the fractional notation of each possibility:

 

For instance, the probability of both being heads or both being tails independently of each other would be:

1/2 * 1/2 = 1/4

 

If the probability of both being heads is 1/4, then the probability of at least one of the coins being tails is the two fractional probabilities added together minus the probability that both will be heads:  1 - 1/4, or 3/4, or .75, or 75%

 

For your second question, 2 4-sided dice.

 

The probability of both dice showing 1 is 1/4 * 1/4 = 1/16

That means the probability of one die showing 1 is :  1/4 + 1/4 - 1/16

1/2 -1/16

7/16 is the probability that at least one die will show 1.