We roll a fair die and compose a box with 11 colored balls. Of these, the number of green balls is equal to the number obtained by rolling the dice. We then proceed by extracting a ball from the box. To calculate
the probability of getting a green ball out of the box Answer
the probability that there are 4 green balls in the box, if the ball we have extracted is green Answer
We now proceed by extracting 2 balls from the box with putting them inside again. To calculate
- the probability of pulling at least one green ball out of the box. Answer
ps. i actually don't know where to start.
Firstly, since we are rolling a fair die, we are likely to get an integer from 1 to 6 with equal probability (1/6 for each). Hence the probability of having 1 green ball in the box is 1/6, same as the probability of having 2, 3, 4 , 5 or 6 green balls in the box.
Hence, P(Getting a green ball out of the box) = (1/6)(1/11) + (1/6)(2/11) + (1/6)(3/11) + (1/6)(4/11) + (1/6)(5/11) + (1/6)(6/11) = (1/6)*(21/11) = 7/22
For the second part, we are conditioning P(4 green balls in the box) on P(Getting a green ball out of the box). P(4 green balls in the box)= P(rolling a 4 on dice) = 1/6 P(P(4 green balls in the box ∩ getting a green ball out of the box) = (1/6)*(4/11) = 2/33
P(4 green balls in the box | Getting a green ball out of the box) = (2/33)/(7/22) = 4/21
For the third part, P(Getting at least 1 green ball) = 1 - P(Getting no green balls)
P(Getting no green balls) = (1/6)(10/11) + (1/6)(9/11) + (1/6)(8/11) + (1/6)(7/11) + (1/6)(6/11) + (1/6)(5/11) = (1/6)*(45/11) = 15/22
P(Getting at least 1 green ball) = 1 - 15/22 = 7/22.