play At a high school, 117 students play basketball, 124 play soccer, 76 student

Question

play At a high school, 117 students play basketball, 124 play soccer, 76 students volleyball, 26 students play both basketball and soccer, 41 students play both basketball and volleyball, 34 students play both soccer and volleyball, 5 students play all three sports, and 59 students are not involved in any of these three sports. Construct a Venn diagram and calculate the following: a) The probability that a student who plays soccer also plays volleyball. b) The probability that a student who plays volleyball also plays basketball. c) The probability that a student who plays basketball and volleyball also plays soccer. ) 2 0 9

Explanation / Answer

here let number of peoble playing basketball are A ; soccer B and volleyball are C.

also as P(AUB) =P(A)+P(B)-P(AnB)

hence

total number of students =student playing at least one game+student playing none =221+59=280

a) probability that a student who play soccer also play volleyball =P(C|B) =P(CnB)/P(B) =34/124=0.2742

b) probability that a student who play volleyball aslo play basketball =P(A|C) =P(AnC)/P(C)=41/76 =0.5395

c)probability =P(B|AnC)=P(AnBnC)/P(AnC) =5/41 =.1220

N(A)= 117 N(B)= 124 N(C)= 76 N(AnB)= 26 N(BnC)= 34 N(AnC)= 41 N(AUB)= 215 N(BUC)= 166 N(AUC)= 152 N(AnBnC) = 5

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