# What is the probability that the ball was labeled

#### Jason000000

##### New member
A tank contains 50 balls. 10 are frosted (F) and labeled (L), 23 are mild (M) and unlabeled, 7 are frosted and not labelled (N), 10 are mild and labeled.

1. A ball is randomly selected from the tank and it was frosted. What is the probability that the ball was labeled?
2. The 1st ball was frosted and the 2nd one was mild (not frosted) What is the probability if we would do two trials?
3. To select a ball was frosted and this ball was not returned to the tank, and select the 2nd one frosted again. What is the probability?

#### Jason000000

##### New member
I finally figured it out .. but I would appreciate if anyone can confirm the answers .. thanx

for Q1. P(L|F) = 10/17

for Q2. P(F) x P(M) = 17/50 x 33/50 = 0.34 x 0.66 = 0.2244

for Q3. P(F1) = 17/50 & P(F2) = 16/49

P(F1|F2) = 17/50 x 16/49 = 0.34 x 0.326 = 0.111

#### Country Boy

##### Well-known member
MHB Math Helper
A tank contains 50 balls. 10 are frosted (F) and labeled (L), 23 are mild (M) and unlabeled, 7 are frosted and not labelled (N), 10 are mild and labeled.

1. A ball is randomly selected from the tank and it was frosted. What is the probability that the ball was labeled?
The ball is one of the 17 frosted balls of which 10 are labeled. The probability this frosted ball is labeled is 10/17.

2. The 1st ball was frosted and the 2nd one was mild (not frosted) What is the probability if we would do two trials?
What is the probability of what? Are you asking "if we take two balls what is the probability that the first is frosted and the second is not"? If so then is the first ball returned to the tank or not?
There are initially 50 balls, 17 of which are frosted. The probability the first ball selected is frosted is 17/50. If that ball is not returned to the tank, there are then 49 balls, 33 of which are not frosted. The probability that the second ball selected is not frosted is 33/49. In this situation the probability the first ball is frosted and the second ball is not is (17/50)(33/49). If the first ball is returned to the tank, the probability second ball is not frosted is (33/50) so the probability of "frosted, not frosted", in that order, is (17/50)(33/50).

3. To select a ball was frosted and this ball was not returned to the tank, and select the 2nd one frosted again. What is the probability?
Initially there are 50 balls in the tank, 17 of which are frosted. The probability the first ball is frosted is 17/50. Since that ball is not returned there are 49 balls, 16 of which are frosted. The probability the second ball is also frosted is 16/49. The probability of two frosted balls, without replacement, is (17/50)(16/49).

#### Jason000000

##### New member
The ball is one of the 17 frosted balls of which 10 are labeled. The probability this frosted ball is labeled is 10/17.

What is the probability of what? Are you asking "if we take two balls what is the probability that the first is frosted and the second is not"? If so then is the first ball returned to the tank or not?
There are initially 50 balls, 17 of which are frosted. The probability the first ball selected is frosted is 17/50. If that ball is not returned to the tank, there are then 49 balls, 33 of which are not frosted. The probability that the second ball selected is not frosted is 33/49. In this situation the probability the first ball is frosted and the second ball is not is (17/50)(33/49). If the first ball is returned to the tank, the probability second ball is not frosted is (33/50) so the probability of "frosted, not frosted", in that order, is (17/50)(33/50).

Initially there are 50 balls in the tank, 17 of which are frosted. The probability the first ball is frosted is 17/50. Since that ball is not returned there are 49 balls, 16 of which are frosted. The probability the second ball is also frosted is 16/49. The probability of two frosted balls, without replacement, is (17/50)(16/49).

#### Wilmer

##### In Memoriam
Why are you asking CBoy that? His answers are SAME as yours!

#### Jason000000

##### New member
Why are you asking CBoy that? His answers are SAME as yours!
because I have extra to his answer:-

P(F) x P(M) = 17/50 x 33/50 = 0.34 x 0.66 = 0.2244
P(F1|F2) = 17/50 x 16/49 = 0.34 x 0.326 = 0.111

is it correct to multiply and get these results?

#### Wilmer

##### In Memoriam
because I have extra to his answer:-

P(F) x P(M) = 17/50 x 33/50 = 0.34 x 0.66 = 0.2244
P(F1|F2) = 17/50 x 16/49 = 0.34 x 0.326 = 0.111

is it correct to multiply and get these results?
Depends on what your teacher expects.
Usually shown as single fraction: 561/2500 and 136/1225.