Answer: [tex]\dfrac{3}{8}[/tex]
Step-by-step explanation:
Formula for probability :-
[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
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 [tex]P(B_1=)\dfrac{5}{5+3}=\dfrac{5}{8}[/tex]
Probability of drawing a black marble from second bag [tex]P(B_2)=\dfrac{6}{6+4}=\dfrac{6}{10}[/tex]
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 :-
[tex]P(B_1)\times P(B_2)\\\\=\dfrac{5}{8}\times\dfrac{6}{10}=\dfrac{3}{8}[/tex]
Hence, the required answer = [tex]\dfrac{3}{8}[/tex]
