Suppose the cards shown are mixed and placed facedown. Think about drawing a card and without replacement drawing a second card. Give the probability in simplest form: P(A, B) = _____
————— ————— ————— —————
| A | | B | | B | | C | ————— ————— ————— —————
————— —————
| C | | C |
----- ------
To find the probability P(A, B) of drawing card A first and card B second, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
In this case, we have a total of 4 cards:
A, B, B, and C.
When drawing the first card, there are 4 cards to choose from. Let's say we draw card A. Now we have 3 cards remaining: B, B, and C.
When drawing the second card without replacement, we have 3 cards left to choose from. Since we want to draw card B as the second card, there are 2 favorable outcomes.
So, the probability P(A, B) can be calculated as the ratio of the number of favorable outcomes to the number of possible outcomes:
P(A, B) = Number of favorable outcomes / Number of possible outcomes
P(A, B) = 2 / 4
Simplifying the fraction, we get:
P(A, B) = 1 / 2
Therefore, the probability of drawing card A first and card B second is 1/2, or 0.5 when expressed as a decimal.