Question

One bag contains three white marbles and five black marbles, and a second bag contains four white marbles and six black marbles. A person draws one marble from each bag. Find the probability that both marbles are black.

Answer 1

5/8 the first bag and 3/5 for the second bag.

Answer 2

Answer: $\dfrac{3}{8}$

Step-by-step explanation:

Formula for probability :-

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

Given : One bag contains 3 white marbles and 5 black marbles, and a second bag contains 4 white marbles and 6 black marbles.

Probability of drawing a black marble from first bag $P(B_1=)\dfrac{5}{5+3}=\dfrac{5}{8}$

Probability of drawing a black marble from second bag $P(B_2)=\dfrac{6}{6+4}=\dfrac{6}{10}$

Since the event of drawing marbles from each bag is independent, then

If a person draws one marble from each bag, then the probability that both marbles are black will be the product of both events :-

$P(B_1)\times P(B_2)\\\\=\dfrac{5}{8}\times\dfrac{6}{10}=\dfrac{3}{8}$

Hence, the required answer = $\dfrac{3}{8}$