Question

Every day a kindergarten class chooses randomly one of the 50 state flags to hang on the wall, without regard to previous choices, We are interested in the flags that are chosen on Monday, Tuesday and Wednesday of next week.
a) Describe a sample space \Omega and a probability measure P to model this experiment.

b) What is the probability that the class hangs Wisconsin's flag on Monday, Michigan's flag on Tuesday, and California's flag on Wednesday.?

c) What is the probability that Wisconsin's flag will be hung at least two of the three days?

Answer 1

Answer:

a.)  P(x = X) = $\frac{1}{50}$

b.) $\frac{1}{50} \times\frac{1}{50} \times\frac{1}{50} = \frac{1}{125000}$

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) = $\frac{1}{50}$ , 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

 = $\frac{1}{50} \times\frac{1}{50} \times\frac{1}{50} = \frac{1}{125000}$

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)

= $(\binom{3}{2}\times \frac{1}{50} \times \frac{1}{50}\times \frac{49}{50}) + (\binom{3}{3}\times \frac{1}{50} \times \frac{1}{50}\times \frac{1}{50})$

= $\frac{147}{125000} + \frac{1}{125000}$

= $\frac{148}{125000}$

= 0.00118