You draw a marble from a jar containing 5 red marbles, 5 green marbles, and 6 blue marbles. Find the probability of drawing a green given that you did not draw a red.
P(green | not red)
The formula for conditional prob is
Prob( A | B) = P(A and B)/P(B)
but you said you were drawing "a marble" suggesting only one is drawn.
To find the probability of drawing a green marble given that you did not draw a red marble, we need to use conditional probability. This can be calculated using the formula:
P(A | B) = P(A ∩ B) / P(B)
Where A and B represent two events, P(A | B) represents the probability of event A occurring given that event B has already occurred, P(A ∩ B) represents the probability of both events A and B occurring together (the intersection), and P(B) represents the probability of event B occurring.
In this case, event A represents drawing a green marble, and event B represents not drawing a red marble.
First, let's calculate the probability of not drawing a red marble.
The total number of marbles in the jar is 5 red + 5 green + 6 blue = 16 marbles.
Therefore, the probability of not drawing a red marble is (total number of non-red marbles) / (total number of marbles) = (5 green + 6 blue) / 16.
So, P(not red) = (5 + 6) / 16 = 11 / 16.
Next, let's calculate the probability of drawing both a green marble and not drawing a red marble (A ∩ B).
To calculate this, we need to find the number of marbles that are both green and not red, which is the number of green marbles.
So, P(green ∩ not red) = number of green marbles / total number of marbles = 5 green / 16.
Therefore, P(green | not red) = P(green ∩ not red) / P(not red).
Plugging in the values, we get:
P(green | not red) = (5 green / 16) / (11 / 16) = 5/11.
So, the probability of drawing a green marble given that you did not draw a red marble is 5/11.