Questions: Mr. and Mrs. Frank just moved into a new home and need to do some landscaping. They are going to purchase one tree, one shrub, and one lilac bush at random from the list to the right. Use this list to complete parts a) through e). Tree Shrubs Lilac bushes Birch (B) Juniper (J) Anabel (A) Dogwood (D) Gold Mop (G) Common (C) Maple (M) Holly (H) Determine the sample space. Choose the correct answer below. A. JA, JC, GA, GC, HA, HC B. DJA, DJC, DGA, DGC, DHA, DHC, MJA, MJC, MGA, MGC, MHA, MHC C. B, D, M, J, G, H, A, C D. BJA, BJC, BGA, BGC, BHA, BHC, DJA, DJC, DGA, DGC, DHA, DHC, MJA, MJC, MGA, MGC, MHA, MHC c) Determine the probability that the Franks select a dogwood tree. The probability is 1/3 (Simplify your answer.) d) Determine the probability that the Franks select a birch tree and a holly shrub. The probability is (Simplify your answer.)

Mr. and Mrs. Frank just moved into a new home and need to do some landscaping. They are going to purchase one tree, one shrub, and one lilac bush at random from the list to the right. Use this list to complete parts a) through e). Tree Shrubs Lilac bushes Birch (B) Juniper (J) Anabel (A) Dogwood (D) Gold Mop (G) Common (C) Maple (M) Holly (H) Determine the sample space. Choose the correct answer below. A. JA, JC, GA, GC, HA, HC B. DJA, DJC, DGA, DGC, DHA, DHC, MJA, MJC, MGA, MGC, MHA, MHC C. B, D, M, J, G, H, A, C D. BJA, BJC, BGA, BGC, BHA, BHC, DJA, DJC, DGA, DGC, DHA, DHC, MJA, MJC, MGA, MGC, MHA, MHC c) Determine the probability that the Franks select a dogwood tree. The probability is 1/3 (Simplify your answer.) d) Determine the probability that the Franks select a birch tree and a holly shrub. The probability is (Simplify your answer.)
Transcript text: Mr. and Mrs. Frank just moved into a new home and need to do some landscaping. They are going to purchase one tree, one shrub, and one lilac bush at random from the list to the right. Use this list to complete parts a) through e). \begin{tabular}{|l|l|l|} \hline Tree & Shrubs & Lilac bushes \\ \hline Birch (B) & Juniper (J) & Anabel (A) \\ Dogwood (D) & Gold Mop (G) & Common (C) \\ Maple (M) & Holly (H) & \\ \hline \end{tabular} Determine the sample space. Choose the correct answer below. A. JA, JC, GA, GC, HA, HC B. DJA, DJC, DGA, DGC, DHA, DHC, MJA, MJC, MGA, MGC, MHA, MHC C. $B, D, M, J, G, H, A, C$ D. BJA, BJC, BGA, BGC, BHA, BHC, DJA, DJC, DGA, DGC, DHA, DHC, MJA, MJC, MGA, MGC, MHA, MHC c) Determine the probability that the Franks select a dogwood tree. The probability is $\frac{1}{3}$ (Simplify your answer.) d) Determine the probability that the Franks select a birch tree and a holly shrub. The probability is $\square$ (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Determining the sample space

The sample space consists of all possible combinations of one tree, one shrub, and one lilac bush. There are 3 trees (Birch, Dogwood, Maple), 2 shrubs (Juniper, Gold Mop), and 2 lilac bushes (Holly, Common). The sample space has 3 * 2 * 2 = 12 possible outcomes. The correct sample space is D.

Step 2: Probability of selecting a dogwood tree

There are 2 shrubs and 2 lilac bushes. If the tree is fixed as Dogwood, there are 2*2 = 4 possible combinations: DJH, DJC, DGH, DGC. Since the total sample space is 12, the probability of selecting a dogwood tree is 4/12 = 1/3.

Step 3: Probability of selecting a birch and holly

There is only one outcome where the Franks select a birch tree and a holly lilac bush: BJH. Since there are 12 total outcomes, the probability is 1/12.

Final Answer:

  1. Sample space: D. BJA, BJC, BGA, BGC, BHA, BHC, DJA, DJC, DGA, DGC, DHA, DHC, MJA, MJC, MGA, MGC, MHA, MHC
  2. Probability of selecting a dogwood tree: 1/3
  3. Probability of selecting a birch tree and holly shrub: 1/12
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