"In Exercises 1-4, identify the sample space of the probabilit...

Question

"In Exercises 1-4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate.

4. Experiment: Guessing the gender(s) of the three children in a family

Event: Guessing that the family has two boys"

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Consider an experiment where you flip a coin 3 times. The experiment target event is getting exactly 2 heads. What is the sample space and how many outcomes are there in this event? Awesome. So it appears for this particular problem we're asked to solve for two separate answers. We're asked to first solve for the sample space, and then we're asked to solve for how many outcomes are there in this specific event, noting once again that our experimental target event is getting exactly 2 heads when you flip a coin 3 times. So with that in mind, our first step that we need to take in order to solve this problem is we need to focus our attention on solving for the sample space. So as you should recall a note, each coin flip has two possible outcomes, either heads or tails. And for 3 flips, the total outcomes are, so I'll call it TO, total outcomes is equal to 2 to the power of 3, which is equal to 8. So now we need to list these outcomes as a sequence. So we need to list them as a sequence of outcomes, which we could write it as such, that the sequence S is equal to heads, heads, heads, heads, heads tail. Heads, tails, heads, tails, heads, heads, heads, tails, tails, tails, heads, tails, tails, tails, heads, and tails, tails, tails. So our second step now is we need to consider the event, which the target event that we're trying to solve for is getting exactly 2 heads. So now at this point, we need to find the outcomes that contain exactly 2 heads. So let's go through the list. So the outcomes that contain exactly 2 heads are heads, heads, tails. Heads, tails, heads, and tails, heads, heads. So, as we can see, these are the only three outcomes that produce exactly 2 heads. So that will mean that our event, which I'll call E, is equal to heads, heads, tails, heads, tails, heads, and tails, heads, heads. Fantastic. So, that means that the number of outcomes in this event. So I'll call it NO, numbers of outcomes is equal to 3, and that is one of our final answers. Hooray, we did it. So now we can recap our final answers because we've officially solved for this problem. So without a doubt, our final two answers will be as follows. The sample space, our first answer is heads, heads, heads, heads, heads, tails, heads, tails, heads, tails, heads, heads. Heads, tails, tails, tails, heads, tail, tails, tails, heads, and tails, tails, tails. And the number of outcomes with exactly 2 heads is 3, and that's it. Those are our final two answers. Hooray, we officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

"In Exercises 1-4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate.
4. Experiment: Guessing the gender(s) of the three children in a family
Event: Guessing that the family has two boys"

Key Concepts

Sample Space

Event

Tree Diagram

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