A manager for a construction firm is bidding on two large contracts. He believes the probability of his firm winning contract #1 is 0.7. If the firm wins contract #1, the probability of the firm also winning contract #2 will be 0.5. If the firm fails to win contract #1, the probability of the firm winning contract #2 will be 0.4. A competitor hears that the firm got the second contract but hears nothing about the first contract. Given that the firm got the second contract, what is the probability that firm also got the first contract?

Do not round intermediate calculations. Round your final answer to four decimals.

Format for probabilities: 0.0000