3. How many different sequences of heads and tails are there...

3. How many different sequences of heads and tails are there if 10 coins are flipped? 4. A teacher asks her 14 third graders to think of a number between 1 and 10. Explain why at least two of them thought of the same number.

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Transcript

00:01 We flip 10 fair coins.

00:02 So i'm going to put n equals 10.

00:04 How many possible outcomes are there? so they've given you a sequence in the next part.

00:09 That would be one possible outcome.

00:11 So it's what we actually see as we flip these coins one after the other.

00:16 So the answer is going to be 2 to the power of 10.

00:20 There are two options on each position, each coin, and to get the total number of options you multiply the number in each coin.

00:27 That's just an application of the multiplication rule from your combinations permutation classes.

00:35 So it's 2 to the power of 10.

00:39 1 ,024 unique strings of heads and tails that you might get.

00:45 Part b, what's the probability of getting this particular sequence in exactly that order? so it's important to note that these coin flips are independent trials.

00:55 Whatever happens on the first flip will not influence the others.

00:59 When that happens, you can multiply the probabilities of each trial to combine the probabilities.

01:06 So the probability of getting heads on the first flip is 0 .5.

01:11 Tails on the second is 0 .5.

01:13 Heads on the third is 0 .5.

01:15 We just have 0 .5 multiplied by itself 10 times.

01:19 1 over 1024...

Question

3. How many different sequences of heads and tails are there if 10 coins are flipped? 4. A teacher asks her 14 third graders to think of a number between 1 and 10. Explain why at least two of them thought of the same number.

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