7 Yasmin has 5 coins. One of these coins is biased with P (heads) \(= 0.6\). The other 4 coins are fair. She tosses all 5 coins once and records the number of heads, \(X\).
- Show that \(\mathrm { P } ( X = 0 ) = 0.025\).
- Show that \(\mathrm { P } ( X = 1 ) = 0.1375\).
The table shows the probability distribution of \(X\).
| \(r\) | 0 | 1 | 2 | 3 | 4 | 5 |
| \(\mathrm { P } ( X = r )\) | 0.025 | 0.1375 | 0.3 | 0.325 | 0.175 | 0.0375 |
- Draw a vertical line chart to illustrate the probability distribution.
- Comment on the skewness of the distribution.
- Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
- Yasmin tosses the 5 coins three times. Find the probability that the total number of heads is 3 .
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