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:
Total number of outcomes=
=
No. of black marbles= 4+6
=
Probability of drawing a black marble=
=
The probability of drawing a black marble from both jars is
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") 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") = 4/(4+4)" "("black"/"black + white")
color(white)("P"("1st is black")) = 4/8
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") = 6/(6+2)" "("black"/"black + white")
color(white)("P"("2nd is black")) = 6/8
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") xx "P"("2nd is black")
color(white)("P"("both black"))=1/2 xx 3/4
color(white)("P"("both black"))=3/8