Vishnu has two jars of marbles, Jar A and Jar B.

• Jar A contains 3 yellow marbles and 2 green marbles.

• Jar B contains 4 yellow marbles and 3 green marbles.

Vishnu flips a fair coin.

• If it lands heads, he picks two marbles at random without replacement from Jar A.

• If it lands tails, he picks two marbles at random with replacement from Jar B.

Given that Vishnu picked one yellow and one green marble, what is the probability that they came from Jar B?

Cards are numbered from 12 to 51 . Two cards are drawn one after the other without replacement. Find the probability that one card is a multiple of $\mathbf{6}$ and the other card is a multiple of $\mathbf{8}$.

If $P(A \cup B)=0.85, P(B)=0.50$ and $P(A \cap B)=0.30$. Then $P\left(A \cap B^{\prime}\right)=$

A company is migrating its database, and two software engineers, Ishaan and Kavya, take turns running a data-sync script that has a constant success rate of $\frac{3}{8}$ per attempt.

If Ishaan initiates the first attempt and they persist until the migration is successful, what is the probability that Kavya is the one who initiates the successful sync?