Rani and Kajal are playing a card game using a standard 52 card deck.
Kajal will pick a card at random. If the card is a black card, she will win $5. If the card is a face card (jack, queen, or king), but not a black card, she will win $3. If she picks anything else, she will lose $10.
The image below shows a standard deck of playing cards.
What is Kajal's expected value of playing this game?

Question

contestada

Respuesta :

abduraaziq1 abduraaziq1 · Answer 1 · 2022-04-25T06:31:12+02:00

Answer:

not answered this question

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-06-30T07:51:07+02:00

Kajal's expected value of playing this game is -$1

The given parameters are:

There are 26 black cards in a standard 52 card decks.

So, we have:

P(Black) = 26/52

There are 6 face cards that are not black in a standard 52 card decks.

So, we have:

P(Face card and not black) = 6/52

There are 20 other cards not in the above categories.

So, we have:

P(Others) = 20/52

The expected value is then calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

This gives

E(x) = 5 * 26/52 + 3 * 6/52 - 10 * 20/52

Evaluate the products

E(x) = 130/52 + 18/52 - 200/52

Evaluate the sum and difference

E(x) = (130 + 18 - 200)/52

This gives

E(x) = -52/52

Evaluate

E(x) = -1

Hence, Kajal's expected value of playing this game is -$1