You have a deck of 52 cards (4 of the 52 cards are aces). Then you randomly sample 5 cards without putting them back. Calculate the probabilities of getting...[br][list][*]exactly 2 aces. [br][/*][*]less than 4 aces. [br][/*][*]more than 1 ace.[br][/*][*]1 to 3 aces.[/*][/list]

[table][tr][td]1.[/td][td][/td][td]Select [size=100]the Hypergeometric [i]Distribution [/i]from the drop-down list.[br][b]Note: [/b]A table providing the probabilites [i]P(X [/i][math]=[/math][size=100][/size][size=100][i] k)[/i] for [math]0 \le k \le n[/math] is created automatically[/size].[/size][/td][/tr][tr][td]2.[/td][td][/td][td]Change the population to [code]52[/code], since there are 52 cards in the deck.[br][/td][/tr][tr][td]3.[/td][td][/td][td]Change the parameter n to [code]4[/code], since there are 4 aces in the deck.[br][/td][/tr][tr][td]4.[/td][td][/td][td]Change the sample to [code]5[/code], since you randomly sample 5 cards.[br][/td][/tr][tr][td]5.[br][/td][td][br][/td][td]Use the table to determine the probability [i]P(X = 2)[/i].[/td][/tr][tr][td]6.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/4/4e/Left_sided.svg/24px-Left_sided.svg.png[/img][/td][td][size=100]Calculate the probability [i]P(X [/i][math]\le[/math][/size][size=100][i] 3)[/i] using the [size=100][i]Left Sided[/i] button.[br][b]Note:[/b] 'Less than 4' means '3 or less aces'.[/size][/size][/td][/tr][tr][td]7.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/b/b3/Right_sided.svg/24px-Right_sided.svg.png[/img][br][/td][td][size=100]Calculate the probability [i]P(2 [/i][math]\le[/math][i] X[/i][/size][size=100][i])[/i] using[size=100] the [i]Right Sided[/i] button.[br][b]Note:[/b] You need to determine the sum of the probabilities of getting 2 or more aces. [/size][/size][/td][/tr][tr][td]8.[br][/td][td][img]https://wiki.geogebra.org/uploads/thumb/0/04/Interval.svg/24px-Interval.svg.png[/img][br][/td][td]Calculate the probability [size=100][i]P(1 [/i][math]\le[/math][i] X [/i][size=100][math]\le[/math][i] 3[/i][/size][size=100][i])[/i] using the [i]Interval [/i]button.[br][/size][/size][/td][/tr][/table]