SOLUTION: If 3/7 of students wear backpacks and 2/5 of students are not in full school uniform, find the probability that a student is wearing a backpack and is in full school uniform.

Question 1121713: If 3/7 of students wear backpacks and 2/5 of students are not in full school uniform, find the probability that a student is wearing a backpack and is in full school uniform.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Define these two events
A = person wears a backpack
B = person is in school uniform

3/7 wear backpacks so P(A) = 3/7
2/5 are not in uniform so 3/5 must be in uniform (since there are only two options), so P(B) = 3/5. Note how 2/5+3/5 = 5/5 = 1. This is like saying if you had 5 students, then 2 would not be in uniform while 3 are in uniform.

Assuming events A and B are independent events, this would mean
P(A and B) = P(A)*P(B)
P(A and B) = (3/7)*(3/5)
P(A and B) = (3*3)/(7*5)
P(A and B) = 9/35

As a fraction, the answer is exactly 9/35. In decimal form, that fraction approximates to roughly 0.25714

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