RI DRV Assignment | Different Socks Problem
RI DRV Assignment | Different Socks Problem
Tutorial
John has \(4\) different pairs of socks in his drawer. Without looking at his drawer, he randomly draws one sock at a time from his drawer without replacement, until he obtains a matching pair. The total number of socks John draws is denoted by \(\mathrm{S}\).
- Show that \(\mathrm{P}(\mathrm{S}=3)=\frac{2}{7}\).
- Explain why \(\mathrm{P}(\mathrm{S}=k)=0\) for \(k=6,7,8\).
- Determine the probability distribution of \(S\).
- Find \(\mathrm{E}(\mathrm{S})\) and \(\mathrm{Var}(\mathrm{S})\).
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Answer:(i) \(\mathrm P(S=3)=\dfrac27\) (ii) The maximum possible value of \(S\) is \(5\) (iii) \(\mathrm P(S=2)=\dfrac17\), \(\mathrm P(S=3)=\dfrac27\), \(\mathrm P(S=4)=\dfrac{12}{35}\), \(\mathrm P(S=5)=\dfrac8{35}\) (iv) \(\mathrm E(S)=\dfrac{128}{35}\), \(\mathrm{Var}(S)=0.968\) to \(3\) significant figures
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