cindy attended her towns annual worm charming competition. contestants are assigned to a square foot of…

cindy attended her towns annual worm charming competition. contestants are assigned to a square foot of land, where they have 30 minutes to \charm\ worms to the surface of the dirt using a single technique. cindy observed contestants charming techniques, and kept track of how many worms surfaced.\n| |5 - 10 worms|11 - 20 worms|\n|--|--|--|\n|tapping the ground|2|2|\n|raking the ground|8|4|\nwhat is the probability that a randomly selected contestant charmed 5 - 10 worms given that the contestant tried raking the ground?\nsimplify any fractions.

cindy attended her towns annual worm charming competition. contestants are assigned to a square foot of land, where they have 30 minutes to \charm\ worms to the surface of the dirt using a single technique. cindy observed contestants charming techniques, and kept track of how many worms surfaced.\n| |5 - 10 worms|11 - 20 worms|\n|--|--|--|\n|tapping the ground|2|2|\n|raking the ground|8|4|\nwhat is the probability that a randomly selected contestant charmed 5 - 10 worms given that the contestant tried raking the ground?\nsimplify any fractions.

Answer

Explanation:

Step1: Identify relevant numbers

We want P(5 - 10 worms | raking). The number of contestants who raked and charmed 5 - 10 worms is 8, and the total number of contestants who raked is (8 + 4=12).

Step2: Calculate conditional - probability

The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In terms of counts, if (A) is the event of charming 5 - 10 worms and (B) is the event of raking, then (P(A|B)=\frac{n(A\cap B)}{n(B)}). Here, (n(A\cap B) = 8) and (n(B)=12). So the probability is (\frac{8}{12}).

Step3: Simplify the fraction

(\frac{8}{12}=\frac{2}{3}).

Answer:

(\frac{2}{3})