Question

Please show all steps and work please

You are assigned to follow up on purchases made through your company’s catalog mailing. You find that 10% ordered a hat and you also find that given someone ordered a hat, 60% also ordered mittens. You also note that 20% of the people who did not order a hat ordered mittens.

A) Complete a Venn diagram for this information.
B) What is the probability that a person ordered neither item?

C) What is the probability that a person ordered a hat or mittens?

D) What is the probability that a person did not order a hat given that they did not order mittens?

Answer 1

Sot Sol 10% ordered a hat (H) ..P(H) = 0.1 Given someone ordered a hat, 60% also ordered millens (m) ..P(m/H)= 0.6 20% of the people who did not order a hat ordered millens. .. p(MIH) - 0.20 P(MIH)= 0.6 Plmnu) 0.6 P(H) PIMH) (0.6) (0.1) - 0.06 ROOSADRESI P (M/H)= 0.20 P( мон') 0.20 P(H') P(mnH')= (0.20) (1-0.1) P(m) - P(mnho = 0.18 Pim) - PLMOH) + 0-18 = 0.06+ 0.18 = 0.24

A) from The above information, we get the following venn diagram. Hat Miltens ol-006 0-24- 0.06 0.06 so.18 0.72 CB P(H OR M) = P(H) +P(M) - P(Ham) 0:1 + 0.24 - 0.06 0.28 B) a person The ordered neither citem probability that P(AUB) 1 - PLAUB) = 1-0.28 0-72 D Here, we need to find P(H'lm') P(Hilm')= P (H'nm') Plm') 1- P(Hum) 11 1- P(m) 0.72 - 0.28 I-0.24 ~ 0.94 74 0.76