Question

q31.) sienna has a bag of 10 marbles. five marbles are blue, four marbles are red, and 1 marble is yellow. sienna draws two marbles from the bag without replacing the marble. what is the probability of drawing a red and a blue marble? answer

Explanation:

Step1: Calculate probability of red - then - blue

The probability of drawing a red marble first is $\frac{4}{10}$. After drawing a red marble, there are 9 marbles left. The probability of then drawing a blue marble is $\frac{5}{9}$. So the probability of red - then - blue is $\frac{4}{10}\times\frac{5}{9}=\frac{20}{90}$.

Step2: Calculate probability of blue - then - red

The probability of drawing a blue marble first is $\frac{5}{10}$. After drawing a blue marble, there are 9 marbles left. The probability of then drawing a red marble is $\frac{4}{9}$. So the probability of blue - then - red is $\frac{5}{10}\times\frac{4}{9}=\frac{20}{90}$.

Step3: Calculate total probability

The probability of drawing a red and a blue marble (in either order) is the sum of the two probabilities above. $\frac{20}{90}+\frac{20}{90}=\frac{40}{90}=\frac{4}{9}$.

Answer:

$\frac{4}{9}$