9 students are seated at random in 3 rows of 3 desks. Let, A= “Anu and Mumu sit in the same row” and B = “Anu and Mumu sit at one of the four corner desks”. Are A and B independent?

Kiyo is creating a table using mosaic tiles chosen and placed randomly. She is picking tiles without looking. How does P(yellow second | blue first) compare to P(yellow second | yellow first) if the tiles are selected without​ replacement? If the tiles are selected and returned to the pile because Kiyo wants a different​ color?

A box contains r red balls and b blue balls. One ball is selected at random and its color is observed. The ball is then returned to the box and k additional balls of the same color are also put in the box. A second ball is then selected at random, Its color is observed & it's returned to the box together with k additional balls of the same color. Each time another ball is selected, the process is repeated. If four balls are selected, whats the probability that the first three balls will be red and the fourth be blue?

Consider a deck of 52 cards with 4 suits and 13 cards (2-10,J,K,Q,A) in each suit. Jack takes one such deck and arranges them in a line in a completely random order. Now he wants to find the number of "Power Trios" in this line of cards. A "Power Trio" is a set of 3 consecutive cards where all cards are either a Jack, Queen or King (J,Q or K). A "Perfect Power Trio" is a set of 3 consecutive cards with exactly 1 Jack, 1 Queen and 1 King (in any order). Find the expected number of Power Trios that Jack will find. Find the expected number of Perfect Power Trios that Jack will find.