A basket contains 4 black, 2 blue, and 5 green balls. Asample of 3 balls is draw

Question

A basket contains 4 black, 2 blue, and 5 green balls. Asample of 3 balls is drawn. Find the probabilities that thesample contains the following. a.) Exactly 2 black balls Answer 14/55 b.) 2 green balls and 1 blue ball 4/33 Please help, I have no idea how to get these answers. A basket contains 4 black, 2 blue, and 5 green balls. Asample of 3 balls is drawn. Find the probabilities that thesample contains the following. a.) Exactly 2 black balls Answer 14/55 b.) 2 green balls and 1 blue ball 4/33 Please help, I have no idea how to get these answers. Please help, I have no idea how to get these answers.

Explanation / Answer

3 balls can be drawn in a total of 11C3 =(11*10*9)/(3*2*1) = 165 ways.
now a) # of ways of drawing 3 balls such that 2 are Black =selecting 2 black balls out of 4 Black * selecting 1 ball out of (2B +5 G) 7 balls
= 4C2 * 7C1 = 6*7 =42
therefore P(exactly 2 black balls) =  # of ways ofdrawing 3 balls such that 2 are Black/Total number of ways ofdrawing 3 balls = 42/165 = 14/55
b) # of ways of drawing 2 green balls and 1 blue ball = # ofways of selecting 2 green balls out of 5 balls * # of ways ofselecting 1 blue ball out of 2 blue ball = 5C2 *2C1 = 10*2 = 20
P(2 green balls and 1 blue ball) = # of ways of drawing 2green balls and 1 blue ball/Total number of ways of drawing 3balls
= 20/165 = 4/33 .
Hope this helps. Feel free to ask for anyclarifications. 3 balls can be drawn in a total of 11C3 =(11*10*9)/(3*2*1) = 165 ways.
now a) # of ways of drawing 3 balls such that 2 are Black =selecting 2 black balls out of 4 Black * selecting 1 ball out of (2B +5 G) 7 balls
= 4C2 * 7C1 = 6*7 =42
therefore P(exactly 2 black balls) =  # of ways ofdrawing 3 balls such that 2 are Black/Total number of ways ofdrawing 3 balls = 42/165 = 14/55
b) # of ways of drawing 2 green balls and 1 blue ball = # ofways of selecting 2 green balls out of 5 balls * # of ways ofselecting 1 blue ball out of 2 blue ball = 5C2 *2C1 = 10*2 = 20
P(2 green balls and 1 blue ball) = # of ways of drawing 2green balls and 1 blue ball/Total number of ways of drawing 3balls
= 20/165 = 4/33 .
Hope this helps. Feel free to ask for anyclarifications.

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