Question

Mr. and Mrs. Frank just moved into a new Tree Shrubs Lilac bushes home and need to do some landscaping. They are going to purchase one tree, one shrub, Birch (8) Gold Mop (G) Sensation (S) and one lilac bush at random from the list to Elm (E) Holly (H) Tinkerbelle (0) the right. Use this list to complete parts a) through e) Dogwood (D) Juniper (J) a) Determine the number of sample points in the sample space The number of points in the sample space is b) Construct a tree diagram and determine the sample space. Construct a tree diagram. Choose the correct answer below O Click here to view diagram a. O Click here to view diagram b. O Click here to view diagram d. O Click here to view diagram Determine the sample space. Choose the correct answer below. O A. EGS, EGT, EHS, EHT, EJS, EJT, DGS, DGT, DHS, DHT, DJS, DJT O B. BGS, BGT, BHS, BHT, BJS, BJT, EGS, EGT, EHS, EHT, EJS, EJT, DGS, DGT, DHS, DHT, DJS, DJT OC. GS, GT, HS, HT, JS, JT OD. B.E.D.G. H.J.S.T

Answer 1

a) The number in the sample points in the sample space is = $3\times3\times2=18$ .

b) The diagram is

n intar T 1. S U 17 나와 \r n I I ID ID L N ㅗ I 1. I - ka B LN. Starts

There are 18 sample points and also from the tree diagram above, we have OPTION B is correct.

c) Number of sample points containing the dogwood tree (given by D) is 6. Thhey are DGS , DGT , DHS , DHT , DJS , DJT. Total number of sample points is 18. So the probability of having dogwood tree is 6/18 = 1/3.

d) The number of sample points containg birch B and holly shrub H is 2. They are BHS , BHT. Total number of sample points is 18. So the probability of having birch and hollyshrub is =2/18 = 1/9.

Or equivalently probbility of having Birch is 1/3. Probbility of having holly shrub is 1/3. Since choosing birch and holly shrub is independent.

So the probability of having birch and hollyshrub is = Probbility of having Birch*Probbility of having holly shrub=(1/3)*(1/3) = 1/9.

e) The sample size with no Tinkerbelle T is 9. They are BGS , BHS , BJS , EGS , EHS , EJS , DGS , DHS , DJS.

So the required probability is 9/18 = 1/2.

Or equivalently the probability of not choosing tinkerbelle = choosing sensation =1/2.