Answer:
X ____ 0 ______ 1 _______ 2
P(x) __ 1/7 _____ 4/7 _____ 2/7
Step-by-step explanation:
Given that :
Number of red balls = 4
Number of Blue balls = 3
Total number of balls = (4 + 3) = 7
Picking without replacement :
Number of picks = 2
1st pick is red :
Probability = (required outcome / Total possible outcomes)
USing combination formula :
nCr = n! / (n-r)! r!
Total possible outcome :
7C2 = 7! / 5!2! = 7*6 / 2 = 42 / 2 = 21
X = number of red
For red = 0;
P(x =0) = required outcome / Total possible outcomes
P(x = 0)
Required outcome : [4C0 * 3C2)]
P(x = 0) = [(4C0 * 3C2)] / 21 = (1*3)/21 = 3/21 = 1/7
P(x = 1)
Required outcome : [4C1 * 3C1)]
P(x = 1) = [(4C1 * 3C1)] / 21 = (4*3)/21 = 12/21 = 4/7
P(x = 2)
Required outcome : [4C2 * 3C0)]
P(x = 2) = [(4C2 * 3C0)] / 21 = (6*1)/21 = 6/21 = 2/7
Hence ;
X ____ 0 ______ 1 _______ 2
P(x) __ 1/7 _____ 4/7 _____ 2/7
