2 Georgie has a red scarf, a blue scarf and a yellow scarf. Each day she wears exactly one of these scarves. The probabilities for the three colours are \(0.2,0.45\) and 0.35 respectively. When she wears a red scarf, she always wears a hat. When she wears a blue scarf, she wears a hat with probability 0.4 . When she wears a yellow scarf, she wears a hat with probability 0.3 .
- Find the probability that on a randomly chosen day Georgie wears a hat.
- Find the probability that on a randomly chosen day Georgie wears a yellow scarf given that she does not wear a hat.