Answer:
14.72% probability that both professors get their grants funded
Step-by-step explanation:
Independent events:
If two events, A and B are independent, the probability of both happening is:

In this question:
Event A: Professor Jane is funded
Event B: Professor Joe is funded.
Professor Jane has a probability of 0.64 of being funded.
This means that 
Professor Joe has probability 0.23 of being funded.
This means that 
What is the probability that both professors get their grants funded

14.72% probability that both professors get their grants funded