# Math 18

**Journal:**

**The PDF file below will have three family pictures on it. The best thing to do is open it and print it out. To see it clearly you have to rotate it clockwise. To do that, you can right-click on the picture and select rotate clockwise. **

CLICK HERE for Family Portraits.pdf

**Once you have a view of the three family pictures, look at the top one. The one with the rare grouping of five consecutive girls followed by six consecutive boys. The caption below the picture states that the chances of this happening is 1 in 2,048. Here’s how they came up with that probability. **

**First, there is only one way you can get 5 girls and 6 boys in that order. To understand this let’s look at a simpler problem. In five children, how many ways can you have 2 girls and then 3 boys in that order. There is only one way, see below.**

GGBBB GBGBB GBBGB GBBBG BGGBB BGBGB BGBBG BBGGB BBGBG BBBGG

The sequences above are all the ways you can have 2 girls and 3 boys for 5 children. Do you see how there are 10 ways, but the first one (underlined and highlighted) is the one we want.**Next, the probability of having a girl is 1/2 and having a boy is 1/2. These events are independent. So, we use the multiplication rule (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32. This fraction is multiplied by how many ways we can get 2 girls and 3 boys in that order, namely 1. Here is the computation =(1)(1/32) = 1/32.****If the problem was: What is the probability of having 2 girls and 3 boys for 5 children? The answer would be (10)(1/32) = 10/32 = 5/16, because there are 10 ways of getting 2 girls and 3 boys if order is not specified.****Now, let’s go back to the original problem. Clearly there is only 1 way you can have 5 consecutive girls followed by six consecutive boys. Since there are 11 children, you would compute (1)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2) = 1/2,048.**

**Problems:**

**1). Look at the family picture in the bottom left-hand corner. Find the probability of having that family of thirteen boys (the mother and father are at the far right and the mother is holding another boy baby).**

**2). Look at the family picture in the bottom right-hand corner. Find the probability of having that family (the mother and father are on both ends of the picture).**

**3). Finally, let me know if there is anything you need help on in regards to probability. It is usually a tricky topic and some students find it difficult. You can ask me a question here, as a journal entry, or you can ask to set up an appointment and we can talk f2f.**

**Important: **

**Once you have formulated your responses for each question above click on “Create Journal Entry” . Label the subject as Journal LM 06 – First name and Last name. For example, I would label my journal entry as “Journal LM 06 – Laurie Kincheloe”. Write your answers for each problem above in the message box. After you are done click “Post”.**