Assume that 20 percent of students have taken calculus in high school. Of those who have taken calculus in high school, 80 percent plan to major in science. Of those who did not take calculus in high school, only 30 percent plan to major in science. What is the probability that a randomly selected student plans to major in science?

The probability that a randomly selected student plans to major in science is 40%

Step-by-step explanation:

Students who take calculus in high school = 20% or 0.2

Of these students, 80% or 0.8 plan to major in science.

That means of these students,

(100 - 80) = 20% or 0.2 do not plan to major in science

Students who do not take calculus in high school = (100 - 20) = 80% or 0.8

Of these students, 30% or 0.3 plan to major in science.

That means of these students,

(100 - 30) = 70% or 0.7 do not plan to major in science.

The probability of students who take calculus in high school and plan to major in science = 0.2 * 0.8

= 0.16

= 16%

The probability of students who take calculus in high school and do not plan to major in science = 0.2 * 0.2

= 0.04

= 4%

The probability of students who do not take calculus in high school and plan to major in science = 0.8 * 0.3

= 0.24

= 24%

The probability of students who do not take calculus in high school and do not plan to major in science

= 0.8 * 0.7

= 0.56

= 56%

All of these probabilities will give 100% of the population.

(16+4+24+56) % = 100%

Therefore, the probability that a randomly selected student plans to major in science = 16% + 24%

= 40%