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 |
————— ————— ————— ————— ————— —————
6 cards in all, so
1/6 * 2/5 = ____
To find the probability of drawing card A and then drawing card B without replacement, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
In this case, there are 2 cards of type A, 2 cards of type B, and 3 cards of type C.
The total number of cards is 2 + 2 + 3 = 7.
To find the probability of drawing card A first, we have:
P(A) = number of cards of type A / total number of cards
= 2 / 7
After drawing card A, there are now 1 card of type A, 2 cards of type B, and 3 cards of type C remaining.
To find the probability of drawing card B without replacement, we have:
P(B|A) = number of cards of type B / total number of remaining cards
= 2 / 6
Therefore, the probability of drawing card A and then drawing card B without replacement is:
P(A, B) = P(A) * P(B|A)
= (2 / 7) * (2 / 6)
= 4 / 42
= 2 / 21
So, P(A, B) = 2 / 21.
To find the probability of drawing card A on the first draw and card B on the second draw without replacement, we need to calculate the probability of each event separately and then multiply them together.
First, let's look at the number of cards of each type:
- There is 1 card labeled A.
- There are 2 cards labeled B.
- There are 3 cards labeled C.
Probability of drawing card A on the first draw:
There is only 1 card labeled A out of a total of 1+2+3=6 cards, so the probability of drawing card A on the first draw is 1/6.
Probability of drawing card B on the second draw:
After removing card A from the deck, there are 5 cards left. Out of these, there are still 2 cards labeled B. Therefore, the probability of drawing card B on the second draw is 2/5.
To find the combined probability, we multiply the probabilities together: 1/6 * 2/5 = (1 * 2)/(6 * 5) = 2/30 = 1/15.
Therefore, P(A, B) = 1/15.