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Which of the following sentences is INCORRECTLY written?
Option B is incorrect because 'give' should be the past participle 'given' in a passive voice construction.
Rewards motivate students to exhibit desired behaviors only when they are things the students genuinely want and value. If a reward holds no appeal for a student, it loses its motivational power. This is why effective teachers personalize or vary their reward systems.
Correct Answer: A — Rewards.
In a game, a player wins Rs. 100 for rolling a 5 or 6 on a fair die, and loses Rs. 50 for any other outcome. He throws the die until he gets 5 or 6, or until he has thrown at most 3 times. Find his expected gain or loss.
$P(\text{win on a throw})=\frac{2}{6}=\frac{1}{3}$, $P(\text{lose})=\frac{2}{3}$.
The player stops as soon as he wins or after 3 throws.
- Win on throw 1: prob $=\frac{1}{3}$; gain $=+100$.
- Win on throw 2 (lost throw 1): prob $=\frac{2}{3}\cdot\frac{1}{3}=\frac{2}{9}$; net $=-50+100=+50$.
- Win on throw 3 (lost throws 1,2): prob $=\frac{2}{3}\cdot\frac{2}{3}\cdot\frac{1}{3}=\frac{4}{27}$; net $=-100+100=0$.
- Lose all 3 throws: prob $=\left(\frac{2}{3}\right)^3=\frac{8}{27}$; net $=-150$.
$E = \frac{1}{3}(100)+\frac{2}{9}(50)+\frac{4}{27}(0)+\frac{8}{27}(-150)$
$=\frac{100}{3}+\frac{100}{9}+0-\frac{1200}{27}$
$=\frac{900}{27}+\frac{300}{27}-\frac{1200}{27}=\frac{0}{27}=\mathbf{0}$
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