5 A bag contains 4 blue discs and 6 red discs. Chloe takes a disc from the bag. If this disc is red, she takes 2 more discs. If not, she takes 1 more disc. Each disc is taken at random and no discs are replaced.
- Complete the probability tree diagram in your Answer Book, showing all the probabilities.
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The total number of blue discs that Chloe takes is denoted by \(X\). - Show that \(\mathrm { P } ( X = 1 ) = \frac { 3 } { 5 }\).
The complete probability distribution of \(X\) is given below.
| \(x\) | 0 | 1 | 2 |
| \(\mathrm { P } ( X = x )\) | \(\frac { 1 } { 6 }\) | \(\frac { 3 } { 5 }\) | \(\frac { 7 } { 30 }\) |
- Calculate \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).