Please include steps 1. An urn contains 6 white (W) and 9 black (B) and 5 green
ID: 3042704 • Letter: P
Question
Please include steps
1. An urn contains 6 white (W) and 9 black (B) and 5 green (G) balls. If 3 balls are randomly selected (assume equally likely outcomes), what is the probability that:
a) Out of the set of three, we select 2 white and 1 black ball
b) Out of the set of three, we select all 3 green balls
c) Out of the set of three, we select all 3 of EQUAL colors (any color)
d) We select a set with at least two colors present in the set of 3 balls.
NOW WE SELECT SEQUENTIALLY AND PAY ATTENTION TO ORDER
e)The first 2 selected are white and the last one is black?
f) The first one is green, the second one is white and the third one is black.
Explanation / Answer
Total balls n = 6 (W) + 9 (B)+ 5 (G) = 20
a ) Out of the set of three, we select 2 white and 1 black ball
Total number of ways to select 3 balls = nC3 = 20C3 = 1140
Number of ways to select 2 whit balls = 6C2 = 15
Number of ways to select 1 black balls = 9C1 = 9
So,
P ( select 2 white and 1 black ball ) = 6C2*9C1 / 20C3 = 0.1184
b) Out of the set of three, we select all 3 green balls.
Number of ways to select 3 green balls = 5C3 = 10
Total ways to select 3 balls = 1140
P( select all 3 green balls ) = 10/1140 = 0.0088
c) Out of the set of three, we select all 3 of EQUAL colors (any color)
We have to find P( select all 3 white or 3 black or 3 green balls )
P( select all 3 of EQUAL colors )
= P( select all 3 white or 3 black or 3 green balls )
= P( select all 3 white balls ) + P( select all 3 black balls ) + P( select all 3 green balls )
= 6C3 / 1140 + 9C3 / 1140 + 5C3 / 1140
= 20/1140 + 84/1140 + 10 / 1140
= 0.1
e )
Probability that first selected ball is white = 6 / 20
Probability that second selected ball is white = 5/19
Probability that third selected ball is black = 9/18
So ,
P(first 2 selected are white and the last one is black )
=6/20 * 5/19 * 9/18
= 0.03947
f )
Probability that first selected ball is green = 5/20
Probability that second selected ball is white = 6/19
Probability that third selected ball is black = 9/18
So,
P ( first one is green, the second one is white and the third one is black )
= 5/20*6/19*9/18
= 0.03947