Question

The following table shows the result of a survey that asked 2850 people whether they were involved in any type of charity work. A person is selected at random from the sample. Find the probability of selecting someone who 1. Frequently Occasionally Not at all Total Male 221 456 795 1472 Female 207 430 741 1378 Total 428 886 1536 2850 a. is frequently or occasionally involved in charity work (2pts) b. is a female given that the person is not at all involved in charity work. (2pts) is frequently involved in charity work and the person is not female. (2pts) c. is occasionally involved with charity work or is a male. d. (Spts) e. Are the events "being male" and "being occasionally involved in charity work" mutually exclusive? Explain. (2pts) f. Are the events "being male" and "being occasionally involved in charity work" independent? Explain showing calculations. (2pts)

Answer 1

Fom the aoven data to tal nomber of people - 2850 Let Bvents Say that on e raventhy SnVolved chostity Ρeople n as A chast ty Peo ple 0ccastonaly invalued n A and B 1Hene mutuall exclosve, 0re Probo b9l6 Now froawontly Gnuolued a pesson charity Ceocesonaly velued in chasaty 1.e, PCA 0B) pCA)+ P(B 428 988 2850 2850 1314 2850 o.46 a female the probo balt ty of 6 Now, o pesson act oull invo luedn not +hat the given Derson fEvents Pemale nvolwed n chaty (A) not fnvolvecl Pn chority W06k. (() Ao A and not Here mutually exclus? ve One P (A ox B) PCA)+P(B)-PCA and B 3 1378 1536 2850 2850 850 LPCA 058) O.762 2850

NoW Pocapently a pesson 9nvolved chastty Gn and the pen son g not female G.e, the n charaty (A) Aseawentty nvolvedl A and B smale. fEveuts, male hwolued or chaority (B)) moteally exclusie penson Here not PLA 0S B) PCA) + P(g ) - P ( A and B) f472 22 2850 a850 1699 2850 O.589 c casfonally Now, probabilly thad a pesson s male chowsby Gnvolved i's E vents Male nvolul onot fmvolved chot ty ca) chasd ty chontty C4) nvolued O en sionally 1472 People occasstonally nvolued An 886 onally nvo lued occassio Male PCA o B) 8&6 2850 2850 2860 0.669

occadionaly beingmale and The events not motually nvoled fn chaord hy wor Qre hawe that exclosive be cause We Can we ho s freavently male parameters fos Separate nve lved occassfonally Gnvawed Sn chanaand oepentely Preavetly Snvo lwed occoupnally nvolved Male Male motuafly exclusdue. They not aup male" and beng NO the occasiorally events not chawoty Snvolued 9n mdependent Ovre x Male 221 t456 +79S 1472 us people o heh get numbor of male .occacstonaly nvo wed Here Inalvded to be to has