Answer:
a.) P(x = X) = [tex]\frac{1}{50}[/tex]
b.) [tex]\frac{1}{50} \times\frac{1}{50} \times\frac{1}{50} = \frac{1}{125000}[/tex]
c.) 0.00118
Step-by-step explanation:
The sample space Ω = flags of all 50 states
a.) Any one of the flags is randomly chosen. Therefore we can write the
probability measure as P(x = X) = [tex]\frac{1}{50}[/tex] , for all the elements of the sample
space, that is for all x ∈ Ω.
b.) the probability that the class hangs Wisconsin's flag on Monday,
Michigan's flag on Tuesday, and California's flag on Wednesday
= [tex]\frac{1}{50} \times\frac{1}{50} \times\frac{1}{50} = \frac{1}{125000}[/tex]
c.) the probability that Wisconsin's flag will be hung at least two of the three days
= Probability that Wisconsin's flag will be hung on two days + Probability that Wisconsin's flag will be hung on three days
= P(x = 2) + P(x = 3)
= [tex](\binom{3}{2}\times \frac{1}{50} \times \frac{1}{50}\times \frac{49}{50}) + (\binom{3}{3}\times \frac{1}{50} \times \frac{1}{50}\times \frac{1}{50})\\[/tex]
= [tex]\frac{147}{125000} + \frac{1}{125000}[/tex]
= [tex]\frac{148}{125000}[/tex]
= 0.00118
