made easy test series - 30 cards are drawn at a time out of 80 playing cards numbered from 1 to 80

Question

 

How to do this question ..please help me guys

Comments

Is the given answer correct?

---

Yess

---

@rekhameena

Please type the question, don't add screenshots unnecessarily !

Answer 1

Suppose you draw a single card, what number do you expect on it?? Let's calculate that first.

it would be, 1/80 * 1 +  1/80 * 2 + 1/80 *3 +.............................. 1/80 * 80

= 1/80 * (80 *81)/2

=40.5

So if you select one card out of 80 cards expected number on it is 40.5

For 30 cards, the Expected value will be, 40.5 *30 =1215

Comments

Thanks

Answer 2

$\text{Total Numbered Cards} = 80$

$\text{Probability of a card being picked} = \Large \frac{3}{8}$

$E[x] = \sum_{i=1}^{k}x_i p_i$

$E[x] =\large  \frac{3}{8} \times 1 + \frac{3}{8} \times 2 + \frac{3}{8} \times 3 +...+\frac{3}{8} \times 80$

$E[x] = \frac{3}{8} \times \left ( 1 + 2 + 3 + 4 +...+80 \right )$

$E[x] = \large \frac{3}{8} \times \left ( \frac{80 \times 81}{2} \right )$

$E[x] = 1215$

Comments

Thanks :)

---

Question saying :-

" the expected value of the sum of numbers on the cards "

---

Shaik Masthan yes calculated the same. your doubt?