An experiment consists of flipping a coin 6 times and noting the number of times that a heads is flipped. Find the sample space S of this experiment.

Question

An experiment consists of flipping a coin 6 times and noting the number of times that a heads is flipped. What is the sample space?

Answer 1

the sample space for flipping a coin 6 times is 2⁶=64 outcomes

 

to get you started...

flip a coin 2 times and the sample space is...

HH, HT, TH, TT

flip a coin 3 times and the sample space is... (put a T and an H with each of the four outcomes you already have)

HHT, HHH

HTT, HTH

THT, THH

TTT, TTH

there are 8 outcomes for flipping a coin 3 times, 2³=8

flip a coin 4 times and the sample space is... (put a T and an H with each of the eight outcomes you already have)

HHTT, HHTH

HHHT, HHHH

HTTT, HTTH

HTHT, HTHH

THTT, THTH

THHT, THHH

TTTT, TTTH

TTHT, TTHH

there are 16 outcomes, 2⁴=16

flip a coin 5 times and the sample space is... (put a T and an H with each of the 16 outcomes to give you 32 outcomes)

I'll leave that up to you.

After doing this, you will have, like I said, 32 outcomes. You then put a T and an H with each of the 32 outcomes for a grand total of 64 outcomes. Good luck.

If order is not important, in other words, if you are looking at combinations and not permutations, then Kyle C. has the solution for you.

 

 

Answer 2

The sample space is the set of all possible outcomes. For this experiment, the possible number of times for a heads are {0, 1, 2, 3, 4, 5, 6}.