The probability that all of the buttons are black when four buttons are picked at random from a which jar contains four black buttons and three, is 1/35.
<h3>What is probability of an event?</h3>
Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
A jar contains four black buttons and three brown buttons. The total number of buttons is,
![4+3=7](https://tex.z-dn.net/?f=4%2B3%3D7)
The probability of picking a black button in the first attempt is,
![P_1=\dfrac{4}{7}](https://tex.z-dn.net/?f=P_1%3D%5Cdfrac%7B4%7D%7B7%7D)
Now, there is total 6 buttons remain in which 3 are black buttons. Thus, the probability of picking black button in second attempt is,
![P_2=\dfrac{3}{6}](https://tex.z-dn.net/?f=P_2%3D%5Cdfrac%7B3%7D%7B6%7D)
Similarly, for the third event,
![P_3=\dfrac{2}{5}](https://tex.z-dn.net/?f=P_3%3D%5Cdfrac%7B2%7D%7B5%7D)
For the fourth event,
![P_4=\dfrac{1}{4}](https://tex.z-dn.net/?f=P_4%3D%5Cdfrac%7B1%7D%7B4%7D)
The probability that all of them are black by the chain rule of probability,
![P=\dfrac{4}{7}\times\dfrac{3}{6}\times\dfrac{2}{5}\times\dfrac{1}{4}\\P=\dfrac{1}{35}](https://tex.z-dn.net/?f=P%3D%5Cdfrac%7B4%7D%7B7%7D%5Ctimes%5Cdfrac%7B3%7D%7B6%7D%5Ctimes%5Cdfrac%7B2%7D%7B5%7D%5Ctimes%5Cdfrac%7B1%7D%7B4%7D%5C%5CP%3D%5Cdfrac%7B1%7D%7B35%7D)
Thus, the probability that all of the buttons are black when four buttons are picked at random from a which jar contains four black buttons and three, is 1/35.
Learn more about the probability here;
brainly.com/question/24756209
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