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Five Heads in a Row and the Next Flip

6th grade nonfiction passage about chance and independent coin flips: 240 words, six questions, an answer key and vocabulary.

6th grade nonfiction chance and independent coin flips 240 words

Five Heads in a Row and the Next Flip

Zara flips a fair coin five times, and it lands on heads every single time. "The next one has to be tails," she announces. "Tails is due!" Her brother Idris shakes his head and explains that the coin has no memory of what it did before.

Idris is right. Each flip of a fair coin is its own event, and what happened before does not change what happens next. Math calls this independence. The chance of heads is 1 out of 2 on every single flip, whether the coin has just landed on heads five times or none at all. So the sixth flip is still a fifty-fifty chance.

Zara's mistake is a very common one, and people even have a name for it, the gambler's fallacy. It feels as though the coin should balance things out, but a coin cannot possibly know what it did earlier.

Does that mean five heads in a row is ordinary? Not quite. To find the chance of a whole streak, multiply the chances together. Half times half, five times, makes 1 out of 32. That is unlikely, but it is far from impossible. If many people each flip a coin five times, a few of them will see exactly this.

Over thousands of flips, heads and tails do come out close to even. This happens not because the coin makes up for early streaks, but because a streak gets lost among all the flips that follow.

Questions

  1. What did Zara think would happen on the next flip? in the text

  2. What is the chance of heads on any single flip of a fair coin? in the text

  3. What does it mean to say the coin has no memory? think about it

  4. What is the gambler's fallacy? in the text

  5. What is the chance of five heads in a row? in the text

  6. Why do heads and tails come out close to even over thousands of flips? think about it

Words to know

independence
when one event does not affect another event
fair
equally likely to land on either side
fallacy
a mistaken idea that seems believable
streak
a run of the same result many times in a row
unlikely
not very likely to happen
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One passage, three levels

The same topic and facts written three ways, so a mixed class can read and talk about one text. Each group’s sheet shows only a shape; the key says which is which.

● Easier · 200 words · Flesch-Kincaid grade 2.3

Zara flips a fair coin five times. It lands on heads every time. "The next one has to be tails," she says. "Tails is due!" Her brother Idris shakes his head. He says the coin has no memory.

Idris is right. Each flip is its own event. What happened before does not change what happens next. Math calls this independence. The chance of heads is 1 out of 2 on every flip. It does not matter if the coin just landed on heads five times. The sixth flip is still fifty-fifty.

Zara made a common mistake. It even has a name: the gambler's fallacy. It feels like the coin should even things out. But a coin cannot know what it did before.

Is five heads in a row ordinary? Not quite. To find the chance of a streak, multiply the chances. Half times half, five times, makes 1 out of 32. That is unlikely, but it is not impossible. If many people flip a coin five times, a few will see this.

After thousands of flips, heads and tails come out close to even. The coin is not making up for the streak. The streak just gets lost among all the later flips.

▲ This passage · 240 words · Flesch-Kincaid grade 4.6

Zara flips a fair coin five times, and it lands on heads every single time. "The next one has to be tails," she announces. "Tails is due!" Her brother Idris shakes his head and explains that the coin has no memory of what it did before.

Idris is right. Each flip of a fair coin is its own event, and what happened before does not change what happens next. Math calls this independence. The chance of heads is 1 out of 2 on every single flip, whether the coin has just landed on heads five times or none at all. So the sixth flip is still a fifty-fifty chance.

Zara's mistake is a very common one, and people even have a name for it, the gambler's fallacy. It feels as though the coin should balance things out, but a coin cannot possibly know what it did earlier.

Does that mean five heads in a row is ordinary? Not quite. To find the chance of a whole streak, multiply the chances together. Half times half, five times, makes 1 out of 32. That is unlikely, but it is far from impossible. If many people each flip a coin five times, a few of them will see exactly this.

Over thousands of flips, heads and tails do come out close to even. This happens not because the coin makes up for early streaks, but because a streak gets lost among all the flips that follow.

■ Harder · 254 words · Flesch-Kincaid grade 6.8

Zara flips a fair coin five times, and on every occasion it lands on heads. "The next one has to be tails," she announces. "Tails is due!" Her brother Idris disagrees, pointing out that a coin has no memory of what it did before.

Idris is correct. Each flip of a fair coin is a separate event, and the outcomes of earlier flips have no influence on the next one. Mathematicians call this independence. The probability of heads remains 1 out of 2 on every individual flip, regardless of whether the coin has just landed on heads five times or not at all. The sixth flip is therefore still an even, fifty-fifty chance.

Zara's error is a remarkably common one, and it even has a name: the gambler's fallacy. It feels as though the coin ought to balance the results, but a coin has no way of knowing what happened earlier.

Does this mean that five heads in a row is perfectly ordinary? Not exactly. To find the probability of an entire streak, you multiply the separate chances together. One half multiplied by itself five times equals 1 out of 32. That outcome is unlikely, yet it is far from impossible. If a large crowd of people each flipped a coin five times, a few of them would witness precisely this.

Over thousands of flips, heads and tails do end up close to even. This is not because the coin compensates for earlier streaks, but because any streak becomes lost among the many flips that follow it.

Download as one PDF

How to use it

  1. Press Read it big (or B) to put the text on the projector, or Full screen (F) to fill the whole screen.
  2. Ask the questions one at a time and use Show answer when the class has decided. A shows or hides every answer.
  3. Print student copy for the class, or Print with answers for yourself.

Ideas for class

  • Before reading, put independence, fair, fallacy, streak and unlikely on the board with their meanings from the Words to know section and have students predict what the text will be about.
  • Read it aloud once while students follow along, then have them reread it alone or with a partner. At a calm 100 words a minute it takes about 2 minutes to read aloud.
  • Use the Read it big button (or B) to put the text on the projector, and Show answer on one question at a time so the class commits to an answer first.
  • Question 3 asks the reader to infer. Ask students to point to the words in the passage that led them to their answer.
  • Ask students to write one question the passage did not answer, then look for the answer in a book or on a classroom screen.
  • Print the student copy for independent work and keep the answer-key copy for yourself.

Related

Questions

What reading level is "Five Heads in a Row and the Next Flip"?

It was written for 6th grade. It has 240 words and works out to a Flesch-Kincaid grade level of about 4.6. That is a formula's estimate from sentence length and syllables, and it is not a Lexile or a guided reading level, so check it against your students.

What do the questions ask?

There are six. 4 ask for something the text says directly and 2 ask the reader to work something out from clues. Each has an answer in the key, and the answers are written as a teacher would accept them, not as the only possible wording.

How long does it take to read?

About 2 minutes read aloud at 100 words a minute. For a one-minute fluency check, paste it into the fluency timer and use the word count.

Can I print it?

Yes. Print student copy gives the passage, the questions with lines to write on, and the word meanings. Print with answers gives the same page with the answers filled in. Both are made in your browser.

Is this passage from a published book?

No. It was written for Peabody Teach, so there is no book to buy and no login to read it.

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