Solution -
The sphere is centered in the cube, so diameter of the sphere is equal to the side of the cube. Hence ,the radius of the sphere is half of the length of the side.
If the length of side of the cibe = a , then radius of the sphere is
Volume of the cube = a³, volume of the sphere = π(radius)³ =
π(
)³
volume of the cube outside the sphere = volume of the cube - volume of the sphere
= π(
)³
=
=a³(1 - )
Answer:
Expected value of drawing a card in this game on the first turn = 6
Step-by-step explanation:
Given - Consider a game in which players draw playing cards one at a time from a standard 52-card deck. If a player draws a face card (a jack, a queen, or a king), the player is awarded 16 points. Any other card drawn earns the player 3 points.
To find - What is the expected value of drawing a card in this game on the first turn?
Formula used -
Expected value, E[x] = ∑ x p(x)
where p(x) is the probability
Proof -
Total cards in a standard deck = 52
Total face cards = 12 (a jack, a queen, or a king)
Other cards = 40
Now,
Probability of getting a face card =
Probability of getting a other card =
So,
Expected value, E[x] = ∑ x p(x)
= (16)() + (3)(
)
=
=
= 6
∴ we get
Expected value of drawing a card in this game on the first turn = 6
So,
The correct option is - B. 6 points