Probability 4 Question 10
10. Given that the drawn ball from $U _2$ is white, the probability that head appeared on the coin is
(a) $\frac{17}{23}$
(b) $\frac{11}{23}$
(c) $\frac{15}{23}$
(d) $\frac{12}{23}$
Passage III
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.
(2009)
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Answer:
Correct Answer: 10. (d)
Solution:
- $P\left(\right.$ Head appeared/white from $\left.U _2\right)$
$$ \begin{aligned} & =P(H) \cdot \frac{\frac{{ }^{3} C _1}{{ }^{5} C _1} \times \frac{{ }^{2} C _1}{{ }^{2} C _1}+\frac{{ }^{2} C _1}{{ }^{5} C _1} \times \frac{{ }^{1} C _1}{{ }^{2} C _1}}{23 / 30} \\ & =\frac{1}{2} \frac{\frac{3}{5} \times 1+\frac{2}{5} \times \frac{1}{2}}{20 / 30} \\ & =\frac{12}{23} \end{aligned} $$
