More on Probability

What happens when probability becomes a bit more tricky?

One of the questions that I posed in my previous post was this:

What is the probability of landing on heads 3 times in a row on a coin toss?

Well, for complicated questions like this, I cannot stress enough how much easier it will be if you construct a probability tree diagram. Here is a tree diagram for the question above:

                                                           H = Heads      T = Tails

Each section represents a possible result from the coin toss. The first coin toss shows 2 possible outcomes: heads or tails. Of course, there is a 1/2 chance of getting either head or tails for each toss. From there, the probability tree shows the possible results of the second and third tosses.

Since our question concerns tossing heads 3 times in a row, we follow the map to view the possible outcomes of tossing heads for each of 3 tosses. Of course, each toss is independent of every other toss so the possibility of tossing heads for each individual toss is always 1/2.

To find the probability of rolling heads 3 times in a row, you simply must multiply the probability of tossing heads for each of the 3 tosses:

  1           X            1           X           1         =       1  
  2                         2                        2                  8

P = 1/8 

Here is another EXAMPLE:

You have a bag that contains 2 blue marbles and 3 red marbles. What is the probability of drawing a red marble and then a blue marble out of the bag without replacement?

Start your tree diagram by  showing the probability of first drawing a blue marble out of the bag. Next show the probability of drawing a red marble first. Your tree diagram should look like this:

Since you are not replacing the first marble you drew from the bag, your # of possible solutions will be 4 instead of 5. Using this new number, show the possible outcomes of your second draw. Your tree diagram should look like this:

 

To determine the chances of drawing a red marble and then a blue marble (in that order), you simply analyze your tree diagram. The probability of drawing a red marble first is 3/5. The probability of drawing a blue marble second is 2/4 (or 1/2). To determine your answer, just multiply these 2 values:

   3         X        1        =       3   
   5                   2                10

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While I know that tree diagrams can be a bit confusing at first, it is a problem-solving strategy that is worth taking the time to learn because it will help you immensely in the future. Click Here to access a site that has further explanations about tree diagrams and even offers you the opportunity to try some sample problems.  

Practice, practice, practice! The more you are exposed to probability problems, the more you will begin to understand them and solving these problems will become second nature!

Thank you for stopping by and enjoy the weekend!

~ Tammy