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

laura 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. laura observed contestants charming techniques, and kept track of how many worms surfaced.\n| |5 - 10 worms|11 - 20 worms|\n|--|--|--|\n|tapping the ground|6|3|\n|raking the ground|2|2|\n|poking small holes in the ground|3|5|\nwhat is the probability that a randomly selected contestant tried poking small holes in the ground given that the contestant charmed 5 - 10 worms?\nsimplify any fractions.

laura 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. laura observed contestants charming techniques, and kept track of how many worms surfaced.\n| |5 - 10 worms|11 - 20 worms|\n|--|--|--|\n|tapping the ground|6|3|\n|raking the ground|2|2|\n|poking small holes in the ground|3|5|\nwhat is the probability that a randomly selected contestant tried poking small holes in the ground given that the contestant charmed 5 - 10 worms?\nsimplify any fractions.

Answer

Answer:

$\frac{3}{11}$

Explanation:

Step1: Find total number of contestants who charmed 5 - 10 worms

$6 + 2+3=11$

Step2: Find number of contestants who poked small holes and charmed 5 - 10 worms

$3$

Step3: Calculate conditional probability

The conditional - probability formula is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequency, if $A$ is the event of poking small holes and $B$ is the event of charming 5 - 10 worms, then the probability that a contestant tried poking small holes given that the contestant charmed 5 - 10 worms is $\frac{\text{Number of contestants who poked small holes and charmed 5 - 10 worms}}{\text{Total number of contestants who charmed 5 - 10 worms}}=\frac{3}{11}$