A card deck for a board game has 20 cards, of which 4 are red, 6 are blue, and 10 are purple. What is the probability of randomly selecting a blue card, then a purple card, without replacement?
Enter your answer as a fraction, rounded to the nearest hundredth, like this: 4/23
3/19
prob(blue, then purple) = (6/20)(10/19) = ....
To find the probability of randomly selecting a blue card, then a purple card without replacement, we need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Finding the probability of selecting a blue card first:
There are initially 20 cards in the deck, and 6 of them are blue. So, the probability of selecting a blue card first is 6/20.
Step 2: Finding the probability of selecting a purple card second:
After removing the blue card from the deck, there are now 19 cards left, and 10 of them are purple. So, the probability of selecting a purple card second is 10/19.
Step 3: Combining the probabilities:
To find the combined probability, we multiply the probability of each event together. Therefore, the probability of selecting a blue card first and then a purple card second is (6/20) * (10/19).
Calculating the solution:
(6/20) * (10/19) = (3/10) * (10/19) = 3/19
Therefore, the probability of randomly selecting a blue card, then a purple card without replacement is 3/19.
To find the probability of randomly selecting a blue card, then a purple card without replacement, we need to calculate two probabilities separately and then multiply them together.
First, let's find the probability of selecting a blue card. There are 4 blue cards out of 20 cards in total. So the probability of choosing a blue card on the first draw is 6/20.
After removing a blue card from the deck, there are now 19 cards left, with 10 purple cards remaining. Therefore, the probability of selecting a purple card on the second draw, without replacement, is 10/19.
To find the probability of both events happening together, we multiply these probabilities: (6/20) * (10/19) = 60/380.
Simplifying the fraction, we get 3/19.
Therefore, the probability of randomly selecting a blue card, then a purple card without replacement is 3/19.