Unknown probability in a biased spinner distribution, the expected score and the probability of a given pair of scores on two spins
Unknown probability in a biased spinner distribution, the expected score and the probability of a given pair of scores on two spins
7 marks
A spinner has sectors that give a score of \(1\), \(2\), \(3\) or \(5\). The spinner is biased, and the table shows the probability distribution of the score, \(X\), on one spin.
| \(x\) | \(1\) | \(2\) | \(3\) | \(5\) |
|---|---|---|---|---|
| \(\mathrm{P}(X=x)\) | \(0.15\) | \(k\) | \(0.35\) | \(0.2\) |
- Find the value of \(k\).[2]
- Find \(\mathrm{E}(X)\).[3]
- The spinner is spun twice. Find the probability that the score is \(5\) on the first spin and \(1\) on the second spin.[2]
Solution:
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Answer:(a) \(k=0.3\) (b) \(\mathrm{E}(X)=2.8\) (c) \(0.03\)
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