There are 7 streets to be named after 7 tree types.
Ash, Elm, Fir, Maple, Oak, Pine, and Spruce.
A city planner randomly selects the street names from the list of 7 tree types.
Compute the probability of each of the following events.
Event The first street is Spruce, followed by Fir then Oak, and then Pine.
Event The first four streets are Maple, Elm, Ash, and Spruce, without regard to order.
Write your answers as fractions in simplest form.

Ask by Hilton Gibson. in the United States

Jan 19,2025

Question

There are 7 streets to be named after 7 tree types.
Ash, Elm, Fir, Maple, Oak, Pine, and Spruce.
A city planner randomly selects the street names from the list of 7 tree types.
Compute the probability of each of the following events.
Event The first street is Spruce, followed by Fir then Oak, and then Pine.
Event The first four streets are Maple, Elm, Ash, and Spruce, without regard to order.
Write your answers as fractions in simplest form.

Ask by Hilton Gibson. in the United States

Jan 19,2025

UpStudy AI · Accepted Answer

To determine the probability of Event $$ \mathrm{A} $$, where the first four streets are named Spruce, Fir, Oak, and Pine in that specific order, we can approach the problem as follows:

1. **Total Possible Arrangements:**
   - There are 7 distinct tree types to be assigned to 7 streets.
   - The total number of possible permutations (arrangements) is $$ 7! = 5040 $$.

2. **Favorable Arrangements for Event $$ \mathrm{A} $$:**
   - The first street must be Spruce, the second Fir, the third Oak, and the fourth Pine. This fixes the first four positions.
   - The remaining three streets can be named using the remaining three tree types (Ash, Elm, Maple) in any order.
   - The number of ways to arrange these three trees is $$ 3! = 6 $$.

3. **Probability Calculation:**
   $$
   P(A) = \frac{\text{Number of Favorable Arrangements}}{\text{Total Possible Arrangements}} = \frac{3!}{7!} = \frac{6}{5040} = \frac{1}{840}
   $$

**Final Answer:**
$$
P(A) = \frac{1}{840}
$$
The probability of Event $$ \mathrm{A} $$ is $$ \frac{1}{840} $$.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Probability Questions