a jar contains red and blue marbles. two marbles are chosen without replacement. the probability of choosing a red marble and then a blue marble is .26, and the probability of selecting a blue marble first is .43. what is the probability of selecting a red marble on the second drawer given that the first marble drawn was blue
To find the probability of selecting a red marble on the second draw given that the first marble drawn was blue, we will use conditional probability.
Let's denote the events as follows:
Event A: Selecting a red marble on the second draw
Event B: Selecting a blue marble on the first draw
Given information:
P(A and B) = 0.26 (probability of choosing a red marble and then a blue marble)
P(B) = 0.43 (probability of selecting a blue marble first)
We can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
Substituting the given values:
P(A|B) = 0.26 / 0.43
Simplifying this:
P(A|B) ≈ 0.6047
Therefore, the probability of selecting a red marble on the second draw given that the first marble drawn was blue is approximately 0.6047 or 60.47%.
To find the probability of selecting a red marble on the second draw given that the first marble drawn was blue, we can use the concept of conditional probability.
Let's denote:
RB - The event of selecting a red marble on the first draw and a blue marble on the second draw.
BR - The event of selecting a blue marble on the first draw and a red marble on the second draw.
We are given two probabilities:
P(RB) = 0.26 (probability of choosing a red marble and then a blue marble)
P(B) = 0.43 (probability of selecting a blue marble on the first draw)
Now, using conditional probability formula:
P(R on second | B on first) = P(RB) / P(B)
We can find P(RB) by rearranging the formula above:
P(RB) = P(R on second | B on first) * P(B)
Since we know P(RB) = 0.26 and P(B) = 0.43:
0.26 = P(R on second | B on first) * 0.43
Now, we can solve for P(R on second | B on first):
P(R on second | B on first) = 0.26 / 0.43
Calculating the result:
P(R on second | B on first) ≈ 0.605 (rounded to three decimal places)
Therefore, the probability of selecting a red marble on the second draw given that the first marble drawn was blue is approximately 0.605, or 60.5%.