There are two jars of marbles. The first jar has 4 black and 4 white marbles. The second jar has 6 black and 2 white marbles. One marble is drawn from each jar. What is the probability of drawing a black marble from both jars?

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There are two jars of marbles. The first jar has 4 black and 4 white marbles. The second jar has 6 black and 2 white marbles. One marble is drawn from each jar. What is the probability of drawing a black marble from both jars?

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Answer 1 · 2018-01-23T16:21:59

$\frac{5}{8}$ $5/8$ .

Explanation:

Total number of outcomes=
$(4 + 4) + (6 + 2)$ $(4+4) + (6+2)$
= $16$ $16$
No. of black marbles= 4+6
= $10$ $10$
Probability of drawing a black marble= $\frac{10}{16}$ $10/16$
= $\frac{5}{8}$ $5/8$

Answer 2 · 2018-01-27T22:33:47

The probability of drawing a black marble from both jars is $\frac{3}{8},$ $3/8,$ or 37.5%.

Explanation:

Since we are making two independent draws, the probability we seek is the product of the probability for success on both draws. In math terms:

$P (both black) = P (1st is black) \times P (2nd is black)$ $"P"("both black")="P"("1st is black") xx "P"("2nd is black")$

Since the draws are both made at random, the probability that the first marble is black is the ratio of black marbles to all marbles:

$P (1st is black) = \frac{4}{4 + 4} (\frac{black}{black + white})$ $"P"("1st is black") = 4/(4+4)" "("black"/"black + white")$

$P (1st is black) = \frac{4}{8}$ $color(white)("P"("1st is black")) = 4/8$

$P (1st is black) = \frac{1}{2}$ $color(white)("P"("1st is black"))=1/2$

Similarly, the probability of drawing a black marble from the second jar is:

$P (2nd is black) = \frac{6}{6 + 2} (\frac{black}{black + white})$ $"P"("2nd is black") = 6/(6+2)" "("black"/"black + white")$

$P (2nd is black) = \frac{6}{8}$ $color(white)("P"("2nd is black")) = 6/8$

$P (2nd is black) = \frac{3}{4}$ $color(white)("P"("2nd is black"))=3/4$

Finally, the probability that both draws are black is the product of these two independent probabilities:

$P (both black) = P (1st is black) \times P (2nd is black)$ $"P"("both black")="P"("1st is black") xx "P"("2nd is black")$

$P (both black) = \frac{1}{2} \times \frac{3}{4}$ $color(white)("P"("both black"))=1/2 xx 3/4$

$P (both black) = \frac{3}{8}$ $color(white)("P"("both black"))=3/8$

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There are two jars of marbles. The first jar has 4 black and 4 white marbles. The second jar has 6 black and 2 white marbles. One marble is drawn from each jar. What is the probability of drawing a black marble from both jars?

2 Answers

Explanation:

Explanation:

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