In a game, 30 cards are drawn at a time out of 80 playing cards numbered from 1 to 80. The expected value of the sum of numbers on the cards drawn is

1215

Open in App

Solution

The correct option is A 1215
Probability of drawing a card = $\frac{1}{80}$

$E (x_{1}) = 1 \times \frac{1}{80} + 2 \times \frac{1}{80} + . . . . . . . + 80 \times \frac{1}{80}$

$= \frac{1}{80} \times \frac{(80) (80 + 1)}{2} = \frac{81}{2}$

Expected value of the sum of numbers on the tickets drawn:
$E (x_{1} + x_{2} + x_{3} + . . . . . . .) = E (x_{1}) + E (x_{2}) + . . . . . + E (x_{30})$

$30 E (x_{1}) = 30 \times \frac{81}{2}$

$= 1215$

Suggest Corrections

Similar questions

Q. From 80 cards numbered 1 to 80, two cards are drawn at random. The probability that the cards have the numbers divisible by 4 is

Q. From a pack of playing cards all cards whose numbers are multiple of 3 are removed. A card is now drawn at random. Then the probability that the card is drawn is an even number is a red card:

Tom and his friends got bored of the game they were playing. They decided to change the rules of the game in which only numbered cards (non-face cards) can be drawn. The score of each player is the product of the numbers on the cards drawn. The scores are written on a sheet of paper after each game. Tom drew the cards as shown in the figure.

Figure: Cards drawn by Tom

Harry was the person writing the scores of all the players, he wrote Tom’s score as 8^x instead of writing it as the product of the numbers on the cards. What is x? (Enter an integral value)

___

Q. Two cards are drawn at random from

10

cards numbered

1

10

. The probability that their sum is even if both the cards are drawn together

Q. Two cards are drawn at random from 10 cards numbered 1 to 10. The probability that their sum is odd if both the cards are drawn together

Join BYJU'S Learning Program

In a game, 30 cards are drawn at a time out of 80 playing cards numbered from 1 to 80. The expected value of the sum of numbers on the cards drawn is 1215

The correct option is A 1215 Probability of drawing a card =180 E(x1)=1×180+2×180+.......+80×180 =180×(80)(80+1)2=812 Expected value of the sum of numbers on the tickets drawn: E(x1+x2+x3+.......)=E(x1)+E(x2)+.....+E(x30) 30E(x1)=30×812 =1215

In a game, 30 cards are drawn at a time out of 80 playing cards numbered from 1 to 80. The expected value of the sum of numbers on the cards drawn is

1215