The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 90 said they had taken physics, 138 said they had taken chemistry and 45 said they had taken both. Thirty-two said they had taken neither. How many recent high school grads were surveyed?
305??
By the inclusion-exclusion principle, the number of grads who have taken at least one of Chemistry or Physics is:
n(P)+n(C)-n(P∩C)
Add this to those who have taken neither is the total number of grads.
(90) + (138) - (48) = 180 + 32 = 212 ??
Correct.
Try to see why it works with the help with the help of a Venn diagram.
thanks a million!
Keep up the good work!
To determine the number of recent high school grads surveyed, we can use a formula called the principle of inclusion-exclusion.
First, we add the number of students who took physics (90) with the number of students who took chemistry (138), which gives us 228 students who have taken at least one of the two subjects.
Next, we subtract the number of students who took both physics and chemistry (45) from the total obtained in the previous step because we have counted them twice. This leaves us with 228 - 45 = 183 students who have taken either physics or chemistry or both.
Finally, we subtract the number of students who took neither subject (32) from the total obtained in the previous step to find the number of students surveyed. Therefore, the number of recent high school grads surveyed is 183 - 32 = 151.
So, the correct answer is 151, not 305.