Mario and Nina each have a bag of marbles, each of which contains 4

Question

Mario and Nina each have a bag of marbles, each of which contains 4 blue marbles, 10 red marbles, and 6 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?

A. 3/4
B. 2/4
C. 1/4
D. 1/8
E. 1/16

A. 3/4
B. 2/4
C. 1/4
D. 1/8
E. 1/16

14101992 · Answer

Mario and Nina each select one marble from their respective bags.

Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble

Probability that either Mario or Nina select a red marble = (10/20)*(10/20) + (10/20)*(10/20) = 2*(1/4)

Probability that either Mario or Nina select a red marble = 1/2

Answer would be B.

P.S. I don't know why option B is 2/4 and not 1/2.

utkarsh240884 · Answer

Mario and Nina each select one marble from their respective bags.

Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble + Probability of both selecting red marble

Probability that either Mario or Nina select a red marble or both select red marble = (10/20)*(10/20) + (10/20)*(10/20) +(10/20)*(10/20) = 3*(1/4)

Probability that either Mario or Nina select a red marble = 3/4

mbaprep2016 · Answer

my under standing says either or means one of the two will have red , so answer should B
Had it been asked at-least 1 red ,we could have choose any one or both in that case it needs to be 3/4

For me answer is B

abhimahna · Answer

I think it should be A.

Probability that either selects a red marble,P(Either) = 1- probability that neither selects a red marble, P(Neither)

Probability that Mario selects non red = 10c1 / 20c1 = 1/2
Probability that Nina selects non red = 10c1 / 20c1 = 1/2
=> P(Either)=1- (1/2*1/2) = 1-1/4= 3/4.

Please correct me if I am missing anything.

Shivam2190 · Answer

Your solution would contain the situation in which both of them select red BUT we want only one of them to pick red.
So the solution would be P=mario(red)*nina(non-red)+nina(red)*mario(non-red)

persist99 · Answer

P(MR or NR)= P(MR)+ P(NR) - P(MR)P(NR)
 =10/20 +10/20 -(10/20)*(10/20) = 20/20 -100/400 = 1-1/4= 3/4

abhimahna · Answer

But no where in the question it is stated that we don't have to consider the both scenario. I believe either A or B could mean A not B, B not A, and A and B.

Please correct me if I am missing anything.

manojach87 · Answer

The key word here is "either".

we have two ways in which either Mario or Nina can select a red marble.
i.e. 
Ether
Mario selects a red marble and Nina selects 0 Red marbles
or Mario select 0 red marbles and Nina selects one Red marble

Now if,
probability of Mario selecting a red marble = PM(R1) 
probability of Nina selecting 0 Red marbles = PN(R0)

probability of Mario selecting 0 red marbles = PM(R0) 
probability of Nina selecting a red marble = PN(R1)

then, in other words 
Probability of getting a red by either Mario or Nina = PM(R1)*PN(R0) + PM(R0)*PN(R1)

EACH bag contains 4 blue marbles, 10 red marbles, and 6 white marbles

Probability of getting a red ball P(R) =   /   = 10/  = 10/20 = 1/2

We know that, 
Probability of not getting a red ball P(R') = 1 - Probability of getting a red ball = 1 - P(R) = 1-  = 1/2

This is true for both Mario and Nina

Hence,

probability of Mario selecting a red marble = PM(R1) = 1/2
probability of Nina selecting 0 Red marbles = PN(R0) = 1/2

probability of Mario selecting 0 red marbles = PM(R0) = 1/2
probability of Nina selecting a red marble = PN(R1) = 1/2

Probability of getting a red by either Mario or Nina = PM(R1)*PN(R0) + PM(R0)*PN(R1) = (  * ) + (  * ) = 1/4 + 1/4 = 2*  = 2/4

janealam · Answer

Mario and Nina each have a bag of marbles, each of which contains 4 blue marbles, 10 red marbles, and 6 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?

A. 3/4
B. 2/4
C. 1/4
D. 1/8
E. 1/16

A. 3/4
B. 2/4
C. 1/4
D. 1/8
E. 1/16

P(A)=10/20=1/2
P(B)=10/20=1/2
P(A&B)=P(A)*P(B)=(1/2)*(1/2)=1/4
P(A or B)=P(A)+P(B)-P(A&B)=1/2+1/2-1/4=3/4

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Vibhatu · Answer

It is not OR probability formula.  Bunuel  please provide the official solution

Posted from my mobile device

Bunuel · Answer

In mathematics, 'or', unless explicitly specified otherwise, means an inclusive 'or', encompassing both condition 1, condition 2, or both conditions. That said, I'd still rephrase the question like this: "What is the probability that Mario or Nina select a red marble?"

Mario and Nina each have a bag of marbles, each of which contains 4

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Mario and Nina each have a bag of marbles, each of which contains 4

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