Answer:
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%
