A coin is tossed 10 times. Calculate the probabilities of getting[br][list][*]3 or less heads[/*][*]more than 5 heads[/*][*]7, 8, or 9 heads[/*][*]exactly 2 heads[/*][/list]Also, find out how many heads you get with a probability of [i]P(a [/i][math]\le[/math] [i]X[/i] [math]\le[/math] [i]b) = 0.8906[/i].

[table][tr][td]1.[/td][td][/td][td]Select [size=100]the [i]Binomial[/i] [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 0[size=100] [math]\le[/math][/size][size=100] [/size][i]k[/i][size=100] [math]\le[/math][/size][size=100] [/size][i]n[/i] is created automatically[/size].[/size][/td][/tr][tr][td]2.[/td][td][/td][td]Change the parameter [i]n[/i] to [code]10[/code], since the coin is tossed 10 times[br][/td][/tr][tr][td]3.[/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] You are determining the sum of the probabilities of getting 0, 1, 2, or 3 heads.[/size][/size][/td][/tr][tr][td]4.[/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(6 [/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 find the sum of the probabilities of getting 6, 7, 8, 9, or 10 heads. [/size][/size][/td][/tr][tr][td]5.[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(7 [/i][math]\le[/math][i] X [/i][size=100][math]\le[/math][i] 9[/i][/size][size=100][i])[/i] using the [i]Interval [/i]button.[/size][/size][/td][/tr][tr][td]6.[br][/td][td][br][/td][td]Use the table to determine the probability [i]P(X = 2)[/i].[/td][/tr][tr][td]7.[br][/td][td][img]https://wiki.geogebra.org/uploads/thumb/0/04/Interval.svg/24px-Interval.svg.png[/img][br][/td][td]Find out for which interval limits the probability equals 0.8906.[br][b]Hint:[/b] You can use the [i]Interval [/i]button and adjust the interval limits by dragging them directly in the graph.[br][/td][/tr][/table]