You choose a tile at random from a bag containing 5 tiles with A, 9 tiles with B, and 4 tiles with C. You pick a second tile without replacing the first. Find each probability.
P (A then C)
P (C then B)
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
5/18 * 4/(18-1) = ?
Use same method for P(C then B)
To find the probabilities, let's first calculate the total number of tiles in the bag. The bag contains 5 tiles with A, 9 tiles with B, and 4 tiles with C, so there are a total of 5 + 9 + 4 = 18 tiles in the bag.
Now, let's calculate each probability:
1. P(A then C):
To find the probability of drawing an A and then a C without replacing the first tile, we need to calculate two separate probabilities and multiply them together.
Probability of drawing an A on the first pick = Number of A tiles / Total number of tiles = 5/18.
After one A tile is drawn, there are now 4 A tiles left in the bag and a total of 17 tiles remaining.
Probability of drawing a C on the second pick = Number of C tiles / Remaining number of tiles = 4/17.
Therefore, P(A then C) = (5/18) * (4/17) = 20/306 = 10/153.
2. P(C then B):
Similarly, to find the probability of drawing a C and then a B without replacing the first tile, we need to calculate two separate probabilities and multiply them together.
Probability of drawing a C on the first pick = Number of C tiles / Total number of tiles = 4/18 = 2/9.
After one C tile is drawn, there are now 3 C tiles left in the bag and a total of 17 tiles remaining.
Probability of drawing a B on the second pick = Number of B tiles / Remaining number of tiles = 9/17.
Therefore, P(C then B) = (2/9) * (9/17) = 18/153 = 2/17.
Hence, the probabilities are:
P(A then C) = 10/153
P(C then B) = 2/17
To find each probability, we need to calculate the probability of the first event happening and then the probability of the second event happening given that the first event has already occurred.
1. P(A then C):
The probability of picking an A first is 5 out of the total number of tiles, which is 5 + 9 + 4 = 18. Once an A has been picked, there are 4 C tiles left out of a total of 17 remaining tiles. Therefore, the probability of picking an A then a C is:
P(A then C) = (5/18) * (4/17) = 20/306 ≈ 0.0654
2. P(C then B):
The probability of picking a C first is 4 out of the total number of tiles, which is 18. Once a C has been picked, there are 9 B tiles left out of a total of 17 remaining tiles. Therefore, the probability of picking a C then a B is:
P(C then B) = (4/18) * (9/17) = 36/306 ≈ 0.1176