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 = \(\dfrac{3}{8}\)
