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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.

2 answers

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:

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

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