Answer:
0.4 ; 0.6125
Step-by-step explanation:
Given the following :
Bag 1 : 75 red ; 25 blue
Bag 2: 60 red ; 40 blue
Bag 3: 45 red ; 55 blue
Probability = (required outcome / Total possible outcomes)
A) since the probability of choosing each bag is equal :
BAG A:
P(choosing bag A) = 1 / total number of bags = 1/3 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100
HENCE, choosing a blue marble from bag A : = (1/3 × 75/100) = 25/300
BAG B:
P(choosing bag B) = 1/3 ;
P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100
HENCE, choosing a blue marble from bag A : = (1/3 × 40/100) = 40/300
BAG C:
P(choosing bag C) = 1/3
P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100
HENCE, choosing a blue marble from bag A : = (1/3 × 55/100) = 55/300
= (25/300) × (40/300) × (55/300) = (25 + 40 + 55)/300 = 120/300 = 0.4
2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each?
BAG A:
P(choosing bag A) = 0.5 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100
HENCE, choosing a blue marble from bag A : = (0.5 × 75/100) = (0.5 * 0.75) = 0.375
BAG B:
P(choosing bag B) = (1-0.5) / 2 = 0.25 ;
P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100
HENCE, choosing a blue marble from bag A : = (0.25 × 40/100) = (0.25 × 0.4) = 0.1
BAG C:
P(choosing bag C) = (1 - (0.5+0.25)) = 0.25
P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100
HENCE, choosing a blue marble from bag A : = (0.25 × 55/100) = 0.25 × 0.55 = 0.1375
= 0.1375 + 0.1 + 0.375 = 0.6125
and get a common denominator of 8 on the right:
. Now simplify and cross-multiply: 39x = -16 andx = -16/39