If you toss 5 fair coins, in how many ways can you obtain at least two heads

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Ammy C.

asked • 09/09/17

Can you please explain I have no idea and im kinda confused

2 Answers By Expert Tutors

(4 choose 2) = 4!/(2!)(2!) = 24/(2*2) = 24/4 = 6

(4 choose 3) = 4!/(3!*1!) = 24/6 = 4

Let's look a the question this way.

Each coin can land on a heads or a tails

Here are the possibilities.  (Each letter is another coin.)

One Tail/3 heads - 4 ways

Two Tails/ two heads - 6 ways

At least 2 heads means 2 heads or 3 heads or 4 heads

There are 6 ways to get 2 heads, 4 ways to get 3 heads and 1 way to get 4 heads.

This is a total of 6+4+1 = 11 ways to get at least 2 heads.

Last updated: 7/13/2022

If you toss 5 fair coins, in how many ways can you obtain at least two heads? ("At least two" is the complement of "zero or one.")

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$\begingroup$

$\binom{10}0 = 1 \rightarrow $ no tails

$\binom{10}1 = 10 \rightarrow $ one tail only

$2^{10} = 1024$

$1024-11 = 1013 $

is this correct?

$\endgroup$

4

The ratio of successful events A = 26 to the total number of possible combinations of a sample space S = 32 is the probability of 2 heads in 5 coin tosses. Users may refer the below solved example work with steps to learn how to find what is the probability of getting at-least 2 heads, if a coin is tossed five times or 5 coins tossed together. Users may refer this tree diagram to learn how to find all the possible combinations of sample space for flipping a coin one, two, three or four times.

Solution

Step by step workout
step 1 Find the total possible events of sample space S S = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, THTTT, TTHHH, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT} S = 32

step 2 Find the expected or successful events A

A = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, TTHHH, TTHHT, TTHTH, TTTHH} A = 26

step 3 Find the probability

P(A) = Successful Events/Total Events of Sample Space
= 26/32 = 0.81 P(A) = 0.81

0.81 is the probability of getting 2 Heads in 5 tosses.