How many marbles are there after drawing the first one? How many of them are black?
6/35
Practice makes perfect
Recall that the probability of an event is the ratio of favorable outcomes to possible outcomes.
Probability=Favorable outcomes/Possible outcomes
In this exercise, we have a box containing 7 marbles, 3 white and 4 black.
We are told that the first marble drawn is black. Out of 7 marbles, 4 marbles are black, which is also the number of favorable outcomes.
P(First black)=4/7 l← ← lBlack marbles Total marbles
The first marble drawn is not replaced, so this event and drawing a second marble are dependent events. Not replacing the first marble means that the number of possible outcomes for the second marble drawn is reduced.
After the black marble is drawn, 6 marbles remain in the bag. This is the new number of possible outcomes.
Since the first marble drawn was black, the number of black marbles has been reduced. The new number of favorable outcomes is 3.
P(Second black)=3/6 l← ← lBlack marbles Total marbles
The second marble drawn is also not replaced, so this event and drawing a third marble are dependent. Not replacing the second marble means that the number of possible outcomes for the third marble drawn is reduced.
After the black marble is drawn, 5 marbles remain in the box. This is the new number of possible outcomes.
Since the second marble drawn was black, the number of white marbles remains unchanged. Therefore, the number of favorable outcomes is 3.
P(Third white)=3/5 l← ← lWhite marbles Total marbles
With this information, we can now calculate P(Black, black, white).
