1 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, \(X\).

1. Show that \(\mathrm { P } ( X = 0 ) = 0.025\).
2. Show that \(\mathrm { P } ( X = 1 ) = 0.1375\). The table shows the probability distribution of \(X\).

   \(r\)	0	1
   \(\mathrm { P } ( X = r )\)	0.025	0.1375	0.3	0.325	0.175	0.0375

3. Draw a vertical line chart to illustrate the probability distribution.
4. Comment on the skewness of the distribution.
5. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
6. Yasmin tosses the 5 coins three times. Find the probability that the total number of heads is 3 .