List the elements in each of the sets. The set of outcomes of tossing three (a) distinguishable

step 1 So in this question we have three distinguishable coins. That means we have each coin having two

List the elements in each of the sets. The set of outcomes...

Key Concepts

Counting Principles

Counting principles such as the multiplication rule play a crucial role in determining the number of outcomes in an experiment. They help calculate the size of the sample space by considering the number of ways each independent coin toss can occur and how these combine, with adjustments made based on whether coins are distinguishable or indistinguishable.

Sample Space

The sample space is the complete set of all possible outcomes in an experiment. In the context of tossing coins, the sample space includes every possible combination of results that can occur during the coin tosses.

Distinguishability

Distinguishability refers to whether individual objects (in this case, coins) are considered different from each other. When coins are distinguishable, each coin is unique (such as being labeled or having different physical attributes), which leads to a different count and arrangement of outcomes compared to when the coins are indistinguishable.

Transcript

00:01 So in this question we have three distinguishable coins.

00:04 That means we have each coin having two possible results that is head or tail and since we have three coins we raise two to the power of three and so we expect eight elements of the set c consisting of the possible variations that we can get when we toss the three coins.

00:29 So either we get a head.

00:34 So let's start with all heads.

00:36 Then introduce the tails from the end.

00:44 So we are just going to use h, h, h, h.

00:50 And introducing a tail from the end with h, h, h, t.

00:55 Another tail.

00:56 So we have h, t, t.

01:01 Then we have o.

01:03 T's and here we're introducing the h's from the end so we have t t h then we have t h then we have t h now we already have h h h so here we are just putting two at the ends then the other end in the in the middle so we have t h and t and we have h t and we have h t t and and h.

01:40 So let's check that we didn't repeat anything.

01:45 H h h h h h h t t t t t t t t h t h t h t h t h t h t h t h t h and h t h t h t h and you can count one, two, three, four, five, six, seven, eight, which is confirmed by our mathematics here.

02:02 So this is the set c consisting of the eight possible variations of results that that we can get when we toss the three coins.

02:14 Now moving on to part b of the question, where we toss three indistinguishable coins.

02:23 Now, since we don't know which coin produced which result, we can only have a certain number of results...

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