Respuesta :
Answer: The required probability is [tex]\dfrac{7}{11}.[/tex]
Step-by-step explanation: Given that a box contains 4 red balls, 5 white balls, and 7 blue balls and we choose two balls at random from the box.
We are to find the probability that neither being red given that neither is white.
Let A and B denote the events that neither of the two balls are red and neither of he two balls are white.
Then, the probabilities of events A and B are given by
[tex]P(A)=\dfrac{5+7}{4+5+7}=\dfrac{12}{16},\\\\\\P(B)=\dfrac{4+7}{4+5+7}=\dfrac{11}{16}.[/tex]
The probability that neither of the two balls are red or white is
[tex]P(A\cap B)=\dfrac{7}{4+5+7}=\dfrac{7}{16}.[/tex]
Therefore, the probability that neither being red given that neither is white is given by
[tex]P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\frac{7}{16}}{\frac{11}{16}}=\dfrac{7}{11}.[/tex]
Thus, the required probability is [tex]\dfrac{7}{11}.[/tex]
