If a bag contains 50 marbles with 28 red ones and 22 blue ones. A marble is picked at random from the bag.what is the probability of picking a red marble after a blue marble was picked first?

after we know that a blue one was picked, there are 21 blues left out of the remaining 49 marbles but still 28 reds, so

prob(next one red) = 28/49

paano naging 28/49?

To calculate the probability of picking a red marble after a blue marble was picked first, we need to consider the number of remaining red marbles and the total number of remaining marbles.

Step 1: Determine the number of red marbles remaining after a blue marble is picked.
Since there are originally 28 red marbles and we picked a blue marble first, there would be 28-1 = 27 red marbles remaining.

Step 2: Determine the total number of marbles remaining after picking the first marble.
After picking the blue marble, there would be a total of 50-1 = 49 marbles remaining.

Step 3: Calculate the probability.
The probability of picking a red marble after a blue marble was picked first would be the number of favorable outcomes (picking a red marble) divided by the number of possible outcomes (remaining marbles).

Therefore, the probability of picking a red marble after a blue marble was picked first is 27/49 or approximately 0.551.

To find the probability of picking a red marble after a blue marble was picked first, we need to understand the concept of conditional probability.

Conditional probability is the measure of the probability of an event occurring given that another event has already occurred. In this case, the event that has already occurred is picking a blue marble first.

To calculate the probability, we can use the formula for conditional probability:

P(A | B) = P(A and B) / P(B)

Where:
P(A | B) represents the probability of event A occurring given that event B has already occurred.
P(A and B) represents the probability of both event A and event B occurring.
P(B) represents the probability of event B occurring.

In our case, event A is picking a red marble, and event B is picking a blue marble first.

Step 1: Calculate the probability of picking a blue marble first.
Out of the total 50 marbles, there are 22 blue marbles.
So, P(B) = 22/50 = 11/25.

Step 2: Calculate the probability of both picking a blue marble first and then picking a red marble afterward.
After picking a blue marble, there will be 49 marbles left, with 28 being red marbles.
So, P(A and B) = 28/49.

Step 3: Use the formula for conditional probability to find P(A | B).
P(A | B) = P(A and B) / P(B) = (28/49) / (11/25).

To simplify this expression, we can multiply the numerator and denominator by the reciprocal of the denominator.
P(A | B) = (28/49) * (25/11) = 700/1078.

Therefore, the probability of picking a red marble after a blue marble was picked first is 700/1078, which can be further simplified if desired.