Question

Plant Types | A B C D E
Number of Seedlings | 100 140 80 60 40
A farmer conducted an inventory on his two square kilometers of rainforest; the results are in the table. He plans on randomly selecting a seedling to experiment on when he goes back to the forest. What is the probability that he will randomly pick a type B plant? Write your answer in the simplest form of a fraction.

Answer 1

To find the probability of randomly selecting a type B plant, we first need to determine the total number of seedlings.

From the table, we have:

- Type A = 100
- Type B = 140
- Type C = 80
- Type D = 60
- Type E = 40

Now, we calculate the total number of seedlings:

\[
\text{Total seedlings} = 100 + 140 + 80 + 60 + 40 = 520
\]

Now that we have the total number of seedlings, we can calculate the probability of selecting a type B plant:

\[
\text{Probability of selecting type B} = \frac{\text{Number of type B seedlings}}{\text{Total number of seedlings}} = \frac{140}{520}
\]

Next, we simplify the fraction \( \frac{140}{520} \):

1. Find the greatest common divisor (GCD) of 140 and 520:
- The prime factorization of 140 is \( 2^2 \times 5 \times 7 \).
- The prime factorization of 520 is \( 2^3 \times 5 \times 13 \).
- The GCD is \( 2^2 \times 5 = 20 \).

2. Divide both the numerator and denominator by their GCD:

\[
\frac{140 \div 20}{520 \div 20} = \frac{7}{26}
\]

Thus, the probability that the farmer will randomly pick a type B plant is:

\[
\boxed{\frac{7}{26}}
\]

Answer 2

wrong