A bag contains 5 purple marbles, 7 yellow marbles, and 3 orange marbles. If two marbles are selected from the bag:
What is the probability that a yellow then an orange are chosen without replacement.
15 total marbles, so
P(yellow,orange) = 7/15 * 3/14
To find the probability of selecting a yellow marble followed by an orange marble without replacement, we need to determine the total number of marbles in the bag and the number of favorable outcomes.
Step 1: Calculate the total number of marbles in the bag
The bag contains 5 purple marbles, 7 yellow marbles, and 3 orange marbles. Therefore, the total number of marbles is 5 + 7 + 3 = 15.
Step 2: Calculate the number of favorable outcomes
To select a yellow marble followed by an orange marble, we first need to calculate the number of ways to select one yellow marble out of 7 and then one orange marble out of the remaining 2.
The number of ways to select one yellow marble out of 7 is denoted by C(7, 1) or "7 choose 1", which can be calculated as 7! / (1! * (7-1)!). This simplifies to 7.
After selecting one yellow marble, there will be 2 orange marbles remaining out of the total 14 marbles. Therefore, the number of ways to select one orange marble out of the remaining 2 is C(2, 1) or "2 choose 1", which can be calculated as 2.
Multiplying these two outcomes together gives us the number of favorable outcomes: 7 * 2 = 14.
Step 3: Calculate the probability
The probability of selecting a yellow marble followed by an orange marble without replacement is the number of favorable outcomes divided by the total number of outcomes.
The total number of outcomes is denoted by C(15, 2) or "15 choose 2". It can be calculated as 15! / (2! * (15-2)!), which simplifies to 105.
Finally, calculate the probability: favorable outcomes / total outcomes = 14 / 105 ≈ 0.1333 (rounded to four decimal places).
Therefore, the probability of selecting a yellow marble followed by an orange marble without replacement is approximately 0.1333 or 13.33%.