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. 30 Experiments with random outcomes (a) Describe a sample space ± 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)   $S=50$

    $P(X)=0.02$

b)  $P(W,M,C)=8*10^-^6$

c)  $P(W_2_3)=1.18*10^-^3$

Step-by-step explanation:

From the question we are told that

Sample space S=50

Sample size n=30

a)Generally the sample space S is

$S=50$

The probability measure is given as

$P(X)=\frac{1}{50}$

$P(X)=0.02$

b)

Generally the probability that  the class hangs Wisconsin’s flag on Monday, Michigan’s flag on Tuesday, and California’s flag on Wednesday is mathematically given as

Probability of each one being hanged is

$P(X)=\frac{1}{50}$

Therefore

$P(W,M,C)=\frac{1}{50} *\frac{1}{50}* \frac{1}{50}$

$P(W,M,C)=\frac{1}{125000}$

$P(W,M,C)=8*10^-^6$

c)Generally the probability that Wisconsin’s flag will be hung at least two of the three days is mathematically given as

Probability of two days hung +Probability of three days hung

Therefore

$P(W_2_3)=^3C_2 (1/50) * (1/50) * (49/50) +^3C_3 (1/50) * (1/50) *(1/50)$

$P(W_2_3)=148 / 125000$

$P(W_2_3)=1.18*10^-^3$