A bag contains seven yellow marbles and two blue marbles. You randomly select two marbles from the bag. What is the probability that both marbles are yellow when you replace each marble before selecting the next marble? Write your answer as a decimal rounded to the nearest thousandth.The probability that both marbles are yellow is about .
Question
A bag contains seven yellow marbles and two blue marbles. You randomly select two marbles from the bag. What is the probability that both marbles are yellow when you replace each marble before selecting the next marble? Write your answer as a decimal rounded to the nearest thousandth.The probability that both marbles are yellow is about .
Solution
To solve this problem, we need to understand that the probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.
Step 1: Calculate the total number of marbles: There are 7 yellow marbles and 2 blue marbles, so the total number of marbles is 7 + 2 = 9.
Step 2: Calculate the probability of drawing a yellow marble: The probability of drawing a yellow marble is the number of yellow marbles divided by the total number of marbles, which is 7/9.
Step 3: Since we are replacing the marble after each draw, the probability of drawing a yellow marble on the second draw is also 7/9.
Step 4: Calculate the probability of both events happening: The probability of both marbles being yellow is the product of the probabilities of each individual event. So, the probability is (7/9) * (7/9) = 49/81.
Step 5: Convert the fraction to a decimal and round to the nearest thousandth: 49/81 = 0.6049382716, which rounds to 0.605 when rounded to the nearest thousandth.
So, the probability that both marbles are yellow is about 0.605.
Similar Questions
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