If I picked a red checker from a bag of 9 black checkers and 6 red checkers, replacing it, and picking a red checker. What would the probability be of each set???
each set?
With replacement, the probability for red remains 6/15 = 2/5
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
stepback fadeaway
I love you
To find the probabilities of picking red checkers in each set, we first need to understand the concept of probability and use the principle of multiplication.
The probability of an event occurring is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In this case, we want to find the probability of picking a red checker from a bag containing 9 black checkers and 6 red checkers.
Set 1: Picking one red checker with replacement
When a checker is replaced after each pick, the total number of checkers in the bag remains the same for each pick. Therefore, the probability of picking a red checker remains constant.
Since there are 6 red checkers out of 15 total checkers, the probability of picking a red checker in any single pick is 6/15 or 2/5.
Set 2: Picking a red checker without replacement
When a checker is not replaced after each pick, the total number of checkers in the bag decreases by 1. Therefore, the probability of picking a red checker changes as we make subsequent picks.
In the first pick, the probability of selecting a red checker is the same as in Set 1, which is 6/15.
After picking a red checker, the number of red checkers decreases by 1 to 5, and the total number of checkers decreases to 14.
In the second pick, the probability of selecting another red checker would be 5/14 since there are now 5 red checkers out of 14 total checkers remaining.
Therefore, the probability of picking a red checker in the second pick, without replacement, is 5/14.
To summarize:
Set 1 (with replacement): The probability of picking a red checker = 6/15 = 2/5
Set 2 (without replacement): The probability of picking a red checker in the first pick = 6/15, and in the second pick = 5/14