Answer:
The probability is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We are going to modeled this problem from the number of heads.
Let be H : ''The number of heads after five flips''
H can assume the following values :
h = 0
h = 1
h = 2
h = 3
h = 4
h = 5
H ~ Bi (n,p)
H ~ Bi (5,0.5)
H can be modeled as a Binomial random variable.
In which p = 0.5 is the success probability (the probability of head in one flip of a fair coin)
n = 5 is the number of times that we flip the coin.
We are also assuming independence in each flip.
The probability function for H is
[tex]P(H=h)=(nCh)p^{h}(1-p)^{n-h}[/tex]
[tex]P(H=h)=(5Ch)0.5^{h}0.5^{5-h}[/tex]
For all the possible values of H
H ≥ 3 is the event that puts Polya on the 7th floor or higher.
Now we calculate the probability of H ≥ 3
[tex]P(H\geq 3)=P(H=3)+P(H=4)+P(H=5)[/tex]
[tex]P(H\geq 3)=(5C3)0.5^{3}0.5^{2}+(5C4)0.5^{4}0.5^{1}+(5C5)0.5^{5}0.5^{0}[/tex]
[tex]P(H\geq 3)=0.3125+0.15625+0.03125=0.5[/tex]
[tex]P(H\geq 3)=\frac{1}{2}[/tex]
Therefore, the probability of each of her next five stops is on the 7th floor or higher is [tex]\frac{1}{2}[/tex]
