SATHEE: Probability 4 Question 9

Probability 4 Question 9

9. The probability of the drawn ball from $U_{2}$ being white, is

(a) $\frac{13}{30}$

(b) $\frac{23}{30}$

(d) $\frac{11}{30}$

Show Answer

Answer:

Correct Answer: 9. (b)

Solution:

Now, probability of the drawn ball from $U_{2}$ being white is

$\begin{aligned} P (white / U_{2}) = P (H) \cdot \frac{^{3} C_{1}}{^{5} C_{1}} \times \frac{^{2} C_{1}}{^{2} C_{1}} + \frac{^{2} C_{1}}{^{5} C_{1}} \times \frac{^{1} C_{1}}{^{2} C_{1}} \\ + P (T) \frac{^{3} C_{2}}{^{5} C_{2}} \times \frac{C_{2}}{^{3} C_{2}} + \frac{^{2} C_{2}}{^{5} C_{2}} \times \frac{^{1} C_{1}}{^{3} C_{2}} + \frac{^{3} C_{1} \cdot^{2} C_{1}}{^{5} C_{2}} \times \frac{^{2} C_{1}}{^{3} C_{2}} \end{aligned}$

$\begin{aligned} = \frac{1}{2} & \frac{3}{5} \times 1 + \frac{2}{5} \times \frac{1}{2} \\ + \frac{1}{2} \frac{3}{10} \times 1 + \frac{1}{10} \times \frac{1}{3} + \frac{6}{10} \times \frac{2}{3} = \frac{23}{30} \end{aligned}$

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Probability 4 Question 9

9. The probability of the drawn ball from U2 being white, is

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9. The probability of the drawn ball from $U_{2}$ being white, is