Suppose you choose a tile from a bag containing 2 A's, 3 B's, and 4 C's. You replace the first tile in the bag and then choose again. Find each probability.
P(A and A)
9 tiles in all, so
P(A,A) = 2/9 * 2/9
i did the quiz and it said the answer was 2/27
Explanation according to the quiz:
P(A and B)
There are 2 A’s and 3 B’s out of a total of 9 tiles.
P(A)=2/9
P(B)=3/9
=1/3
P(A and B)=
2/9•1/3=2/27
To find the probability of choosing two A's in a row, we need to determine the probability of choosing one A and then replacing it before choosing again.
Step 1: Find the probability of choosing the first A:
There are a total of 2 A's out of a bag with a total of 2 A's, 3 B's, and 4 C's. So, the probability of choosing the first A is 2/9.
Step 2: Find the probability of choosing the second A:
After replacing the first A, there is still a total of 2 A's out of a bag with a total of 2 A's, 3 B's, and 4 C's. So, the probability of choosing the second A is also 2/9.
Step 3: Find the probability of both events happening (P(A and A)):
To find the probability of both events happening, we multiply the probabilities of each event occurring. Therefore, P(A and A) = (2/9) * (2/9) = 4/81.
Therefore, the probability of choosing two A's in a row is 4/81.
To find the probability of selecting two A's in a row, you need to find the probability of selecting an A on the first draw and then the probability of selecting an A on the second draw, assuming you replaced the first tile back into the bag each time.
Step 1: Find the probability of selecting an A on the first draw.
There are 2 A's in the bag out of a total of 9 tiles (2 A's + 3 B's + 4 C's). Therefore, the probability of selecting an A on the first draw is 2/9.
Step 2: Find the probability of selecting an A on the second draw.
Since you replaced the first tile back into the bag, the total number of tiles remains the same. So, there are still 2 A's in the bag, but now there are 10 tiles in total. Therefore, the probability of selecting an A on the second draw is 2/10.
Step 3: Find the probability of selecting A and A.
To find the probability of two independent events occurring, you multiply their individual probabilities. So, the probability of selecting A and A is:
P(A and A) = P(A on first draw) * P(A on second draw)
= (2/9) * (2/10)
= 4/90
= 2/45
Therefore, the probability of selecting two A's in a row is 2/45.