When Greta's mother goes shopping, the probability that she takes Greta with her is 52 . When Greta goes shopping with her mother she gets an ice cream 70% of the time. When Greta does not go shopping with her mother she gets an ice cream 30% of the time.
Determine the probability that:
a. when Greta's mother goes shopping, she buys Greta an ice cream
b. Greta went shopping with her mother, given that her mother buys her an ice cream.