Respuesta :
Answer:
The probability that both chips are the same color is 0.322 or 32.2%.
Step-by-step explanation:
Given:
Urn 1:
Number of red chips, n(R1) = 3
Number of black chips, n(B1) = 2
Number of white chips, n(W1) = 5
Total number of chips, N₁ = 3 + 2 + 5 = 10
Urn 2:
Number of red chips, n(R2) = 2
Number of black chips, n(B2) = 4
Number of white chips, n(W2) = 3
Total number of chips, N₂ = 2 + 4 + 3 = 9
Probability of getting a red chip from urn 1 is given as:
[tex]P(R1)=\frac{n(R1)}{N_1}=\frac{3}{10}[/tex]
Probability of getting a red chip from urn 2 is given as:
[tex]P(R2)=\frac{n(R2)}{N_2}=\frac{2}{9}[/tex]
Probability of getting a black chip from urn 1 is given as:
[tex]P(B1)=\frac{n(B1)}{N_1}=\frac{2}{10}[/tex]
Probability of getting a black chip from urn 2 is given as:
[tex]P(B2)=\frac{n(B2)}{N_2}=\frac{4}{9}[/tex]
Probability of getting a white chip from urn 1 is given as:
[tex]P(W1)=\frac{n(W1)}{N_1}=\frac{5}{10}=\frac{1}{2}[/tex]
Probability of getting a white chip from urn 2 is given as:
[tex]P(W2)=\frac{n(W2)}{N_2}=\frac{3}{9}=\frac{1}{3}[/tex]
Now, drawing chips of same color means drawing either 2 red or 2 black or 2 white chips.
So, probability of drawing chips of same color is given as:
[tex]P(same)=P(R1)\cdot P(R2)+P(B1)\cdot P(B2)+P(W1)\cdot P(W2)\\[/tex]
Plug in the given values and simplify. This gives,
[tex]P(same)=(\frac{3}{10}\times \frac{2}{9})+(\frac{2}{10}\times \frac{4}{9})+(\frac{1}{2}\times \frac{1}{3})\\\\P(same)=\frac{1}{15}+\frac{4}{45}+\frac{1}{6}\\\\P(same)=\frac{1\times 6}{15\times 6}+\frac{4\times 2}{45\times 2}+\frac{1\times 15}{6\times 15}\\\\P(same)=\frac{6}{90}+\frac{8}{90}+\frac{15}{90}\\\\P(same)=\frac{6+8+15}{90}=\frac{29}{90}=0.322[/tex]
Therefore, the probability that both chips are the same color is 0.322 or 32.2%.
The probability that both chips are the same color is [tex]0.322[/tex]
Probability :
Given that,
Urn I has three red chips, two black chips, and five white chips.
Urn II has two red, four black, and three white.
When One chip is drawn at random from each urn.
Then, the probability that both chips are the same color is,
[tex]P(E)=P_{1}(R)P_{2}(R)+P_{1}(B)P_{2}(B)+P_{1}(W)P_{2}(W)\\\\P(E)=\frac{3}{10}*\frac{2}{9}+ \frac{2}{10}*\frac{4}{9}+\frac{1}{2}*\frac{1}{3}\\\\P(E)=\frac{1}{15}+\frac{4}{45}+\frac{1}{6} \\\\P(E)=\frac{29}{90}=0.322[/tex]
Thus, the probability that both chips are the same color is [tex]0.322[/tex]
Learn more about the probability here:
https://brainly.com/question/25870256
