A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec

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QUESTION #5:

A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability that the first ball picked up is odd numbered?

(A) 0
(B) 1/3
(C) 1/2
(D) 2/3
(E) 1

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Kurtosis · Accepted Answer

We are given that, out of the three balls selected 2 are odd and 1 is even.
We can have the following arrangements: OOE, OEO, EOO
P(1st ball is odd numbered) = 2/3

Answer: D

sahil7389 · Answer

A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability that the first ball picked up is odd numbered?

(A) 0
(B) 1/3
(C) 1/2
(D) 2/3
(E) 1

Answer-D
Selecting the balls either Even or Odd is having probability 50/100=1/2
We have already selected 3 balls with 2 odd numbers and 1 even number.
So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability is 2/3.

AmoyV · Answer

Probability of picking 1 even an 2 odd balls = 1/2 * 1/2 * 1/2 
Now we have 2 repetitions of odd balls so we have to multiply the probability with 3!/2!
Total probability = 1/2*1/2*1/2*3
=3/8

Probability of picking the 1st ball as odd = 1/2 * 1/2 * 1/2
Now the 2nd and 3rd draw could be counted in 2! ways. Also, we need to divide the entire equation by 2! since we have 2 repetitions (odd nos). So, total probability is 1/8.

This is a conditional probability. Given that we have 2 odd and 1 even ball, what is the probability of picking the 1st ball as odd

1/8 / 3/8
1/8 * 8/3
=1/3

Answer: B

ShristiK · Answer

The question essentially asks the probability of getting the first ball as odd out of three possible outcomes: OOE, EOO, OEO.
Here, we can see that the first ball is odd in two instances out of three.
Therefore, the probability of getting the first ball as odd is: 2/3
Ans. D

Deepak66 · Answer

Correct answer is D i.e. 2/3 because two odd and one even can be arranged in 3!/2!=3 ways OOE,OEO and EOO out of these only two cases are favorable. So probability will be 2/3

Bunuel · Answer

JAMBOBREE OFFICIAL SOLUTION:

If 3 balls are selected such that 2 of them have odd numbers on them and the other has even number, then there are 3 cases:
Odd Odd Even - OOE,
Odd Even Odd - OEO,
Even Odd Odd - EOO

Clearly, of these total 3 cases, there are 2 favorable cases in which the first ball picked is odd. Thus, required probability is 2/3.

Answer: D.

bumpbot · Answer

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