3. Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 blue balls. Find the probability mass function (P. M.F.) for the number of red balls draw.

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

answer: the dogs need to shift their focus to human scent.

its because the dogs being trained are for search and rescue thus they need to be able to track humans and their specific scent

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hope this : )