There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar

Probability of the first ball being orange = 2/5
The first all is not replaced, hence the total number of balls for the second pick = 1/4
Therefore the total probability is 2/5 x 1/4 = 1/10

Hence E

The probability that at least one marble picked is orange is equal to 1 - the probability that zero orange marbles are picked. This probability is basically saying that we're first picking one of the three blue marbles from 5 total marbles and then picking one of two blue marbles from a total of four marbles. Assume that we're not replacing any marbles back into the bag.

This means P = 1 - 3/5*2/4 = 1 - 6/20 = 1 - 3/10 = 7/10.

Choice A

There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability that at least one will be orange?

A) 7/10
B) 3/5
C) 2/5
D) 3/10
E) 1/10

Method 1

Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue)*P(Second Marble is Blue) = 1- (3/5)(2/4) = 7/10

Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10

Method 3

Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10

Answer : A

Yes the above explanation is right. I misread

1st ball orange and 2nd ball orange =2/5*1/4=1/10
1st ball blue and 2nd ball orange =3/5*2/4=3/10
1st ball orange and 2nd ball blue= 2/5*3/4=3/10

so total probability = 1/10+3/10+3/10=7/10
Hope this is clear.

The correct answer is A.
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the probability of none of the marble will be orange is \(\frac{3}{5}\frac{2}{4}\)=\(\frac{3}{10}\)
the probability that at least one will be orange 1-\(\frac{3}{10}\) = \(\frac{7}{10}\)
the answer is A

That was eazy!


(2C1*3C2+2C2)/5C2 = 7/10

Hope it's clear!

At least one means there are two possible scenarios in this case:

1. 1 orange + 1 blue : 2C1 x 3C1 = 6 ways
2. 2 orange + 0 blue: 2C2 = 1 way

6 + 1 = 7

Without restrictions:

5C2 = 10 ways

7 / 10

Answer is A.
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