6.
The discrete random variable \(D\) has the following probability distribution
| \(d\) | 10 | 20 | 30 | 40 | 50 |
| \(\mathrm { P } ( D = d )\) | \(\frac { k } { 10 }\) | \(\frac { k } { 20 }\) | \(\frac { k } { 30 }\) | \(\frac { k } { 40 }\) | \(\frac { k } { 50 }\) |
where \(k\) is a constant.
- Show that the value of \(k\) is \(\frac { 600 } { 137 }\)
The random variables \(D _ { 1 }\) and \(D _ { 2 }\) are independent and each have the same distribution as \(D\).
- Find P \(\left( D _ { 1 } + D _ { 2 } = 80 \right)\)
Give your answer to 3 significant figures.
A single observation of \(D\) is made.
The value obtained, \(d\), is the common difference of an arithmetic sequence.
The first 4 terms of this arithmetic sequence are the angles, measured in degrees, of quadrilateral \(Q\) - Find the exact probability that the smallest angle of \(Q\) is more than \(50 ^ { \circ }\)