A bag of pofmäs contains 2/3 white granules and 1/3 yellow granules. Only 1/2 of the white grain will pop, while 2/3 of the yellow grain will pop. A grain of wheat is randomly selected from that bag; this grain pops when placed in the puffing machine. Determine the probability that the grain was drawn white.
P(white,pop) = 2/3 * 1/2 = 1/3
P(yellow,pop) = 1/3 * 2/3 = 2/9
P(pop) = 1/3 + 2/9 = 5/9
so, what do you think?
I think it's right. thank you
To determine the probability that the grain was drawn white, we need to consider the ratio of white grains to the total number of grains. Let's go step by step:
Step 1: Let's assume that the total number of grains in the bag is a multiple of 6 (since the fraction 2/3 + 1/3 can be simplified to 2/6 + 1/6).
Step 2: Since 2/3 of the grains are white, the number of white grains can be represented by (2/3) * total number of grains.
Step 3: Only 1/2 of the white grains will pop, so the number of white grains that will pop is (1/2) * (2/3) * total number of grains.
Step 4: Similarly, 2/3 of the yellow grains will pop, so the number of yellow grains that will pop is (2/3) * (1/3) * total number of grains.
Step 5: The total number of grains that will pop is the sum of white grains that will pop and yellow grains that will pop: [(1/2) * (2/3) * total number of grains] + [(2/3) * (1/3) * total number of grains]
Step 6: To find out the probability of drawing a white grain, we need to divide the number of white grains that will pop by the total number of grains that will pop.
Probability of drawing a white grain = [(1/2) * (2/3) * total number of grains] / [(1/2) * (2/3) * total number of grains] + [(2/3) * (1/3) * total number of grains]
Simplifying the expression, we get:
Probability of drawing a white grain = (1/6) / [(1/6) + (2/9)]
Now, you can simplify the expression further and calculate the probability using a calculator or by converting the fractions to decimals.