Suppose one card is selected at random from an ordinary deck of 52 playing cards.
Let
A= event a diamond is selected
B=event a club is selected
Determine P(A|(not B))
DrBob said it is 1/3
but how did he get it?
I keep getting answer
1 or 21/26
If you eliminate the 1/4 of the cards that are clubs, one third of what is left are diamonds.
To determine the probability of event A occurring, given that event B did not occur, we need to calculate the probability of A intersection (not B), divided by the probability of (not B).
Let's break it down step by step:
Step 1: Calculate the probability of event A occurring (selecting a diamond). There are 13 diamonds in a standard deck of 52 cards, so the probability of selecting a diamond is 13/52, which simplifies to 1/4.
Step 2: Calculate the probability of event B not occurring (not selecting a club). There are 13 clubs in a standard deck of 52 cards, so the probability of not selecting a club is 39/52, which simplifies to 3/4.
Step 3: Calculate the probability of A intersection (not B) occurring (selecting a diamond and not selecting a club). Since diamonds and clubs are disjoint sets (no overlap), the probability of A intersection (not B) is equal to the probability of A multiplied by the probability of not B, which is (1/4) * (3/4) = 3/16.
Step 4: Finally, calculate the probability of A occurring, given that not B occurred. This can be found by dividing the probability of A intersection (not B) by the probability of not B, which is (3/16) / (3/4) = 1/4.
Therefore, the correct answer is 1/4, not 1/3.
To determine the probability of event A (a diamond is selected) given that event B (a club is not selected) has occurred, we need to find the number of favorable outcomes and the total number of possible outcomes.
In this case, we need to find the probability of selecting a diamond when a club is not selected.
The total number of cards in a deck is 52, with 13 diamonds and 13 clubs.
The number of favorable outcomes, which is selecting a diamond when a club is not selected, is 13 diamonds.
The probability of event A (picking a diamond) given that event B (not picking a club) has occurred can be calculated as:
P(A|(not B)) = P(A and (not B)) / P(not B)
The probability of selecting a diamond and not selecting a club (A and (not B)) is the same as the probability of selecting a diamond because the two events are mutually exclusive. Therefore, P(A and (not B)) is simply the probability of selecting a diamond, which is 13/52 or 1/4.
The probability of not picking a club (not B) can be calculated as:
P(not B) = 1 - P(B)
The probability of picking a club is 13/52 or 1/4, so the probability of not picking a club is 1 - (1/4) = 3/4.
Finally, we can calculate P(A|(not B)):
P(A|(not B)) = (P(A and (not B))) / (P(not B))
P(A|(not B)) = (1/4) / (3/4)
P(A|(not B)) = 1/3
Therefore, the probability of event A (selecting a diamond) given that event B (not selecting a club) has occurred is 1/3.