Suppose that we know that pe1 38 and that pe2 39 how

Question

Question: 1. Suppose that we know that P(E₁) = 3/8 and that P(E₂) = 3/9. How large and how small might P(E₁ and E₂) and P(E₁ or E₂) be?

2. You have Xs and Os (nine of each) in a bag near a tic-tac-toe board. You arbitrarily select an X or an O, and then you place it arbitrarily on the board. Toss your letter back in the bag, shake the bag, and again arbitrarily select an X or an O and place it arbitrarily on the board.

(a) Consider the event in which you select the same letter twice; define a random variable corresponding to this event and compute its expected value.

(b) Consider the event of placing both letters in the same row; define a random variable corresponding to this event and compute its expected value.

(c) Consider the event of placing both letters in the same column; define a random variable corresponding to this event and compute its expected value.

(d) What is the probability that both letters are placed in the same column and in the same row?

(e) What is the probability that the same letter is selected twice and both are placed in the same row?

(f) Are any two of these three events independent?