How do you calculate cumulative probability? If one tosses a coin 3 times, what are the odds that 1 toss will be "heads"?

1 Answer
EZ as pi
Dec 2, 2017

#3/8#

Explanation:

There are two ways I can think of:

Method 1

In order to have exactly one head in three rows, it means the other two throws are tails. Consider how this could happen:
The 'head could be on the first, second, or third throw.

#P(H,T,T) or P(T,H,T) or P(T,T,H)#

#P(H) =P(T) = 1/2#

#P(H,T,T) or P(T,H,T) or P(T,T,H)#

#= (1/2xx1/2xx1/2)+(1/2xx1/2xx1/2)+(1/2xx1/2xx1/2)#

#= 1/8+1/8+1/8 =3/8#

Method 2

Write down all the #8# possible outcomes for #3# throws:

#HHH#

#color(blue)(HT T, HTH, T TH)#

#THH, THT, HHT#

#T T T#

Of the #8# outcomes there are #color(blue)(3)# which have one head.

#P("one head") = 3/8#

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