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.
What is probability of an event?
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,
[tex]4+3=7[/tex]
The probability of picking a black button in the first attempt is,
[tex]P_1=\dfrac{4}{7}[/tex]
Now, there is total 6 buttons remain in which 3 are black buttons. Thus, the probability of picking black button in second attempt is,
[tex]P_2=\dfrac{3}{6}[/tex]
Similarly, for the third event,
[tex]P_3=\dfrac{2}{5}[/tex]
For the fourth event,
[tex]P_4=\dfrac{1}{4}[/tex]
The probability that all of them are black by the chain rule of probability,
[tex]P=\dfrac{4}{7}\times\dfrac{3}{6}\times\dfrac{2}{5}\times\dfrac{1}{4}\\P=\dfrac{1}{35}[/tex]
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;
https://brainly.com/question/24756209
#SPJ1
