A coffee roaster has $\mathbf{1 2}$ rare coffee beans with intensity scores ranked from $\mathbf{1}$ (mildest) to $\mathbf{1 2}$ (strongest).

You choose 7 beans at random and line them up from mildest to strongest:

$$ C_1< C_2< C_3< C_4< C_5< C_6< C_7 $$

What is the probability that the third bean $\left(C_3\right)$ has an intensity score of exactly 4 ?

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 $P\left(A \cap B^{\prime}\right)=$