1· The following table shows the division played in for 120 major league basebal
ID: 3048466 • Letter: 1
Question
1· The following table shows the division played in for 120 major league baseball players. Total central western Division Players (a) 12 points] IfI first pick a ball player at random, and then (with replacement of the first player) pick Eastern 30 40 50 120 another player at random, what is the probabili ty that both of them are from the central division? Show your work by writing down the formula of the basic rule that you use, and then fill in the numbers and calculate the answer (b) 12 points] IfI first pick a ball player at random, and then (without replacement of the first player) pick another player at random, what is the probability that both of them are from the eastern division? Show your work by writing down the formula of the basic rule that you use, and then fill in the numbers and calculate the answer.Explanation / Answer
(a) Here as if i pick first player at random, then probability of getting the player from centra division is
Pr(First player is from Western division) = Number of players from central division/ total players = 40/120 = 1/3 = 0.33
Now, we replaced the player so Now, if pick a player at random, the player from central division is
Pr(Second player is from Western division) = Number of players from central division/ total players = 40/120 = 1/3 = 0.33
Probability that both are from Central division = 0.33 * 0.33 = 1/9 = 0.1111
(b) Now we will pick players at random,
Pr(Choosing first player from eastern division) = Total eastern division player/ Total player = 30/120 = 1/4 = 0.25
Now, we are not replacing this first player, so now only 29 eastern player left out of 119 total players
Pr(Choosing second player from eastern division) = 29/119 = 0.2437
Pr(Both players from eastern division) = 0.25 * 0.2437 = 0.061
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