Tips And Tricks And Shortcut For Venn Diagrams

Question 1

In a class of 260 seniors, 93 study Spanish, 95 study Chemistry, 165 study Mathematics, 18 study Spanish and Chemistry, 75 study Chemistry and Math, 20 study Math and Spanish and 15 study all three subjects. Make a Venn diagram to illustrate the data and then find the probability that a student selected at random studies Spanish but not Maths.

Options

(a) 0.121
(b) 0.0192
(c) 0.269
(d)0.387

Correct Option (A)

Explanations

•  Spanish  but not Maths and Chemistry

P(S∩M’∩C’) = \frac{70}{260} = \frac{7}{26} = 0.269

• Maths and Chemistry but not Spanish

P(M∩C∩S′)= \frac{60}{230} = \frac{3}{13} = 0.231

• None of these subject

P(M′∩C′∩S′) = \frac{5}{260} = \frac{1}{52}

• Spanish, given that he/she studies Math

P(S, M)\frac{P(S\cap M’)}{P(M)} = \frac{\frac{20}{260}}{\frac{165}{260}} = 0.121