Statistics WA3: The U.S governors are selected at random without replacement

The U.S governors are selected at random without replacement

  1. Find the probability that the first is a republican and the second a democrat

Let R represent republican and D represent democratic

P (R1&D1) =P(R1)× (D2/R1)

P (R1) =30/50

P (D2&R1) = 20/49

P (R1 &D1) = P(R1)×(D2&R1)= 30/50×20/49= 0.244

Therefore, the probability that first is republican and the second is a democrat is o.244.

  1. Find the probability that both are Republican

P (R1&R2) = P(R1)× (R2/R1)

P (R1) =30/50

P (R2&R1) = 29/49

P (R1 &R2) = P(R1)×(R2&R1)= 30/50×29/49= 0.355

The probability that both are republican is 0.355

  1. Draw a tree diagram for thus problem similar to the one shown in Fig. 4.25 on page 194

29/49 R2(R1&R2)= 30/50×29/40= 0.355

R1 20/49 D2 (R1&D2)30/50×20/49= 0.244

30/50

30/49 R2(D1&R2)= 20/50 ×30/49=0.244

20/50

D1 19/49 R2 D1&D2)=20/50×19/49=0.244

  1. What is the probability that the two governors selected have the same political-party affiliation

P(R1&R2)+ P(D1&D2)= 0.355+0.155=0.510

  1. What is the probability that the two governors selected have different political –part affiliation

P(R1&D2)+ P(D1&D2)= 0.244+0.244=0.490

4.186

a. Find P(C1)

P(C1)= 9.3/61.4= 0.151

b. Find P(C1/S2)

P(C1/S2)= 13/25.8= 0.050

c. Are events C1 and S2 independent? Explain your answer

If P(C1/S2)= P(C1) then events are independent, because 0.050≠0.151 events are dependent

d. Is the events that an injured person is male independent of the event that an injured person was hurt at home? Explain your answer.

Male injured person= 35.6

Home injured person= 21.4

P(C2)= 21.4/61.4= 0.348

P(S1)=35.6/61.4=0.579

If P(C2&S2)= P(C2) the events are independent, but because 0.348×0.579≠ 0.348 events are independent.

4.188

a. find the probability P(G1), P(F1), AND P(G1&F1).

P(G1)= 0.419/1= 0.419

P(F1)=0.582/1= 0.582

P(G1&F1)=0.300/1=0.300

b. Use the special multiplication rule to determine whether event G1 and F1 are independent

If P(G1&F1)=P(G1)×P(F1) when the events are independent, but substituting the values in a. into the equation we see that 0.300±0.419×0.582, so events are depend.

Reference

Delucchi, M. (2006). The efficacy of collaborative learning groups in an understanding statistics course. College teaching, 54, 244-248.

Muth, J. E. (2006). Basic Statistics and Pharmaceutical Statistical Application (Vol. 2). New York: Chapman & Hall. CRC Press.