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Grade 12 · Math

Find a binomial coin-toss probability

Combine independent equally likely trials with a count of favorable position sets.

8 authored questions + worked example

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Worked example

A fair coin is tossed 4 times independently. What is the probability of exactly 1 heads? Give a fraction in simplest form.

Answer & why

Answer:

There are 16 equally likely ordered outcomes. Choose the 1 head positions in 4 ways: probability = 1/4.

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All questions

All 8 authored questions for this skill.

Question 1

A fair coin is tossed 7 times independently. What is the probability of exactly 2 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 128 equally likely ordered outcomes. Choose the 2 head positions in 21 ways: probability = 21/128.

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Question 2

A fair coin is tossed 8 times independently. What is the probability of exactly 3 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 256 equally likely ordered outcomes. Choose the 3 head positions in 56 ways: probability = 7/32.

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Question 3

A fair coin is tossed 4 times independently. What is the probability of exactly 1 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 16 equally likely ordered outcomes. Choose the 1 head positions in 4 ways: probability = 1/4.

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Question 4

A fair coin is tossed 4 times independently. What is the probability of exactly 2 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 16 equally likely ordered outcomes. Choose the 2 head positions in 6 ways: probability = 3/8.

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Question 5

A fair coin is tossed 5 times independently. What is the probability of exactly 2 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 32 equally likely ordered outcomes. Choose the 2 head positions in 10 ways: probability = 5/16.

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Question 6

A fair coin is tossed 5 times independently. What is the probability of exactly 3 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 32 equally likely ordered outcomes. Choose the 3 head positions in 10 ways: probability = 5/16.

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Question 7

A fair coin is tossed 6 times independently. What is the probability of exactly 2 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 64 equally likely ordered outcomes. Choose the 2 head positions in 15 ways: probability = 15/64.

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Question 8

A fair coin is tossed 6 times independently. What is the probability of exactly 3 heads? Give a fraction in simplest form.

A hint

Count ways to choose the head positions, then divide by all equally likely toss sequences.

Answer & why

Answer:

There are 64 equally likely ordered outcomes. Choose the 3 head positions in 20 ways: probability = 5/16.

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