# Math Help - Probability question

1. ## Probability question

Hi, here is the question:
Ahmed goes to school either by car or by bicycle. If it is raining at 7:30am in themorning, the probably of Ahmed going to school by car is 0.7. If it is not raining in the morning, the probability that he goes to school by car is 0.4. The probability of rain at 7.30 in the morning is 0.1. A day is selected at random.
a) Find the probabilty that Ahmed cycles to school.
I've done this part correctly and the answer is 0.57.
b) Ahmed's teacher sees him cycling to school one morning. Find the probability that it was raining at 7.30 that morning.
I'm really stuck on this question, any help would be appreciated!!

2. Given R represents the event it is raining and C represents the event of cycling then $\displaystyle P(R|C) = \frac{P(R\cap C)}{P(C)}$

3. I know that the probability of C would be 0.57, but I'm not sure how you'd go about finding the probability of R intersect C, so I'd really appreciate it if you could explain that to me. Also, the answer to the question is 1/19, if that's helpful.