The frequency of purple pollen cones is 0.34 in a population of Virginia pine (Pinus virginiana). In the same population, the frequency of four needles per fascicle is 0.67. If these two traits are independent, what is the probability that a single pine tree has both purple pollen cones and four needles per fascicle? (calculate to 2 decimals)

P(p and f) = 0.23

Explanation: The frequency of a specific trait is also the probability of that trait appearing in that population. So:

Probability of purple pollen cones: P(p) = 0.34

Probability of four needles per fascicle: P(f) = 0.67

Using multiplication rule:

P(p and f) = P(p)*P(f)

P(p and f) = 0.34*0.67

P(p and f) = 0.23

The probability of having both purple and four needles is 0.23

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