a jar contains 4 white chips, 5 purple chips and 1 black chip. chips are selected randomly one at at time and are not replaced. What is the probability of choosing a purple then black chip?

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To find the probability of choosing a purple chip first and then a black chip, we need to determine the total number of chips and the number of favorable outcomes, which is the number of ways to choose a purple chip followed by a black chip.

The total number of chips is the sum of all the chips in the jar: 4 white chips + 5 purple chips + 1 black chip = 10 chips.

To calculate the probability, we need to consider the two steps separately:

Step 1: Choosing a purple chip
There are 5 purple chips out of the total 10 chips in the jar. So, the probability of choosing a purple chip on the first draw is 5/10.

Step 2: Choosing a black chip
After selecting the purple chip on the first draw, there are now only 9 chips in the jar, including 1 black chip. So, the probability of choosing a black chip on the second draw is 1/9.

Now, we can multiply the probabilities of both steps to find the overall probability:

Probability of choosing a purple then black chip = (5/10) * (1/9) = 5/90 = 1/18

Therefore, the probability of choosing a purple chip first and then a black chip is 1/18.

To find the probability of selecting a purple chip followed by a black chip, we need to calculate the probability of each event separately and then multiply them together.

Step 1: Calculate the probability of selecting a purple chip.
There are a total of 4 + 5 + 1 = 10 chips in the jar, and 5 of them are purple. Therefore, the probability of selecting a purple chip on the first draw is 5/10.

Step 2: Calculate the probability of selecting a black chip.
After one purple chip is drawn, we are left with a total of 10 - 1 = 9 chips in the jar. Out of these 9 chips, there is only 1 black chip. Therefore, the probability of selecting the black chip on the second draw is 1/9.

Step 3: Multiply the probabilities.
To find the probability of both events happening, we multiply the probabilities from steps 1 and 2: (5/10) * (1/9) = 5/90 = 1/18.

Therefore, the probability of choosing a purple chip followed by a black chip is 1/18.

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