- In a quiz, a team gains 10 points for every question it answers correctly and loses 5 points for every question it does not answer correctly. The probability of answering a question correctly is 0.6 for each question. One round of the quiz consists of 3 questions.
The discrete random variable \(X\) represents the total number of points scored in one round. The table shows the incomplete probability distribution of \(X\)
| \(x\) | 30 | 15 | 0 | - 15 |
| \(\mathrm { P } ( X = x )\) | 0.216 | | | 0.064 |
- Show that the probability of scoring 15 points in a round is 0.432
- Find the probability of scoring 0 points in a round.
- Find the probability of scoring a total of 30 points in 2 rounds.
- Find \(\mathrm { E } ( X )\)
- Find \(\operatorname { Var } ( X )\)
In a bonus round of 3 questions, a team gains 20 points for every question it answers correctly and loses 5 points for every question it does not answer correctly.
- Find the expected number of points scored in the bonus round.