A group of men and women are asked if they prefer summer or winter. The resulting two-way frequency table is shown below.
Category Summer Winter
Women 85 32
Men 70 51
Use the data in the table to find each probability.
P(woman)
P(woman or summer)
P(woman and summer)
P(woman|summer)
P(woman) = (number of women) / (total number of people) = (85 + 32) / (85 + 32 + 70 + 51) = 117 / 238 = 0.4916
P(woman or summer) = (number of women or number of people who prefer summer) / (total number of people) = (85 + 32 + 85 + 70) / (85 + 32 + 70 + 51) = 272 / 238 = 1.1429
P(woman and summer) = (number of women who prefer summer) / (total number of people) = (85) / (85 + 32 + 70 + 51) = 85 / 238 = 0.3571
P(woman|summer) = (number of women who prefer summer) / (total number of people who prefer summer) = (85) / (85 + 70) = 85 / 155 = 0.5484