Question

a survey of a sample of recent hires at major tech companies aims to investigate which applicants are most likely to be hired for positions in data science. the findings of the survey are presented in the venn diagram below. a venn diagram with an unlabeled universal set contains two intersecting circles labeled graduate degree and 10 years experience that divides the universal set into four regions labeled as follows, where the label is given first and the content is given second: graduate degree only, 16; graduate degree and 10 years experience only, 4; 10 years experience only 20; outside the circles only, 7. given that a random data scientist from the sample has less than ten years of experience in the industry, what is the probability that they have a graduate degree in a relevant discipline? provide the final answer as a simplified fraction.

Answer 1

The probability that a random data scientist from the sample has a graduate degree in a relevant discipline, given that they have less than ten years of experience, is 1/6.

Step-by-step explanation:

To find the probability that a random data scientist from the sample has a graduate degree in a relevant discipline, given that they have less than ten years of experience, we need to consider the intersection of the graduate degree and less than ten years of experience regions on the Venn diagram.

According to the given information, the region labeled 'graduate degree and 10 years experience only' contains 4 individuals, and the region labeled '10 years experience only' contains 20 individuals.

Since we are interested in the probability of having a graduate degree among data scientists with less than ten years of experience, we need to find the ratio of the number of individuals in the intersection region (graduate degree and 10 years experience only) to the total number of individuals with less than ten years of experience (sum of the two intersection regions):

Probability = Number of individuals in intersection region / Total number of individuals with less than ten years of experience

Probability = 4 / (4 + 20) = 4 / 24 = 1/6