There are 3 pencil boxes containing 3 colored pencils - Red, Green and Blue.
Pencil box 1 contains: 24 green pencils. Red pencils are 4 more than blue pencils.
Probability of selecting 1 red pencil is 4/13
Pencil box 2 contains: Total pencils are 8 more than 7/13 of pencils in pencil box 1. -
Probability of selecting 1 red pencil is 1/3. The ratio of gred pencils to blue pencils is 1:2
Pencil box 3 contains: Red pencils equal total number of green and blue pencils in pencil
box 2. Green
pencils equal total number of green and red pencils in pencil box 2. Probability of selecting
1 blue pencil is 3/14.
1 pencil each is chosen 'from pencil box 1 and pencil box 2, What is the probability that 1 is
red and other blue?
Answers
Answer:
probability that 1 is red and other blue = 25/117
Step-by-step explanation:
Pencil box 1 contains:
G = 24 green pencils.
Red pencils are 4 more than blue pencils
=> R = B + 4
=> Total = G + R + B = 24 + B + 4 + B = 2B + 28
Probability of selecting 1 red pencil is 4/13
= (B + 4)/(2B + 28) = 4/13
=> 13B + 52 = 8B + 112
=> 5B = 60
=> B = 12
R = 12 +4 = 16
Total = 24 + 12 + 16 = 52
Pencil Box 1 : G = 24 , R = 16 , B = 12 & Total = 52
Pencil box 2 contains:
Total pencils are 8 more than 7/13 of pencils in pencil box 1. -
=> Total = (7/13)*52 + 8 = 28 + 8 = 36
Probability of selecting 1 red pencil is 1/3.
=> R/Total = 1/3 => R/36 = 1/3 => R = 12
=> G + B = Total - R = 36 - 12 = 24
The ratio of green pencils to blue pencils is 1:2
=> B = 2G => G + 2G = 24 => 3G = 24 => G = 8
B = 16
Pencil Box 2 : G = 8 , R = 12 , B = 16 & Total = 36
Pencil box 3 contains:
Red pencils equal total number of green and blue pencils in pencil box 2.
R = 8 + 16 = 24
Green pencils equal total number of green and red pencils in pencil box 2.
G= 8 + 12 = 20
Probability of selecting 1 blue pencil is 3/14.
B / (24 + 20 + B) = 3/14
=> 14B = 132 + 3B
=> 11B = 132
=> B = 12
Pencil Box 3 : G = 20 , R = 24 , B = 12 & Total = 56
1 pencil each is chosen 'from pencil box 1 and pencil box 2
probability that 1 is red and other blue
= red from 1st & blue from 2nd + blue from 1st & red from 2nd
= (16/52) * (16/36) + (12/52)(12/36)
= ( 256 + 144)/(52 * 36)
= 400/ (52 * 36)
= 25/(13 * 9)
= 25/117
probability that 1 is red and other blue = 25/117
Answer:
Step-by-step explanation: