Question

A coin is flipped five times. Find the number of possible sets of heads and tails that have at most 3 heads

Answer 1

Answer:

$Sets = 27$

Step-by-step explanation:

Given

$Coin = 1$

$Toss = 5$

Required

Number of outcomes with at most 3 heads

First, we list out the sample space of a toss of coin 5 times

$(HHHHH)$, $(HHHHT)$, $(HHHTT)$, $(HHTTT)$, $(HTTTT)$, $(TTTTT)$, $(TTTTH)$, $(TTTHH)$, $(TTHHH)$, $(THHHH)$, $(HTHTH)$, $(THTHT)$, $(HHTHH)$, $(TTHTT)$, $(HTTHT)$, $(THHTH)$, $(THHHT)$, $(HTTTH)$, $(THHTT)$, $(HTTHH)$, $(HHTTH)$, $(TTHHT)$, $(TTHTH)$, $(HHTHT)$, $(HTHTT)$, $(THTHH)$, $(THTTH)$, $(HTHHT)$, $(HTHTT)$, $(THTHH)$, $(HHHTH)$, $(TTTHT)$

Next, we list out all outcomes with at most 3 heads

, , $(HHHTT)$, $(HHTTT)$, $(HTTTT)$, $(TTTTT)$, $(TTTTH)$, $(TTTHH)$, $(TTHHH)$, , $(HTHTH)$, $(THTHT)$, , $(TTHTT)$, $(HTTHT)$, $(THHTH)$, $(THHHT)$, $(HTTTH)$, $(THHTT)$, $(HTTHH)$, $(HHTTH)$, $(TTHHT)$, $(TTHTH)$, $(HHTHT)$, $(HTHTT)$, $(THTHH)$, $(THTTH)$, $(HTHHT)$, $(HTHTT)$, $(THTHH)$, $(TTTHT)$

So, the number of set is:

$Sets = 27$