Question

Find the probability of each event

Answer 1

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,

$4+3=7$

The probability of picking a black button in the first attempt is,

$P_1=\dfrac{4}{7}$

Now, there is total 6 buttons remain in which 3 are black buttons. Thus, the probability of picking black button in second attempt is,

$P_2=\dfrac{3}{6}$

Similarly, for the third event,

$P_3=\dfrac{2}{5}$

For the fourth event,

$P_4=\dfrac{1}{4}$

The probability that all of them are black by the chain rule of probability,

$P=\dfrac{4}{7}\times\dfrac{3}{6}\times\dfrac{2}{5}\times\dfrac{1}{4}\\P=\dfrac{1}{35}$

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

#SPJ1