Question

three - fourths of a research team worked in a lab while one - fourth of the team worked near a pond. of the researchers who worked near the pond, 14% collected insects. what is the probability that a randomly chosen researcher worked near the pond and collected insects? probability = %

Explanation:

Step1: Calculate the proportion of the team that worked near the pond

The proportion of the team that worked near the pond is \(\frac{1}{4}= 0.25\) (in decimal form).

Step2: Calculate the probability of working near the pond and collecting insects

We use the formula for the probability of two - independent events \(P(A\cap B)=P(A)\times P(B)\). Let \(A\) be the event of working near the pond and \(B\) be the event of collecting insects. We know \(P(A) = 0.25\) and \(P(B|A)=0.14\) (since among those who worked near the pond, 14% collected insects). Then \(P(A\cap B)=0.25\times0.14\)

$$0.25\times0.14=\frac{25}{100}\times\frac{14}{100}=\frac{25\times14}{10000}=\frac{350}{10000} = 0.035$$

To convert this decimal to a percentage, we multiply by \(100\), so \(0.035\times100 = 3.5\)

Answer:

\(3.5\)