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Kennedy3449
20.09.2020 •
Mathematics
There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3 has 45 red and 55 blue marbles. Now a bag is chosen at random and a marble is also picked at random. 1) What is the probability that the marble is blue? 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? Make sure to clearly define your probabilistic events and mathematically show how different probability laws and rules that you learned in class could be applied to solve the problems.
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Ответ:
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
Ответ:
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