Answer:
The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Let 'S' be the sample space associated with the drawing of a card
n (S) = 52C₁ = 52
Let E₁ be the event of the card drawn being a king

Let E₂ be the event of the card drawn being a queen

But E₁ and E₂ are mutually exclusive events
since E₁ U E₂ is the event of drawing a king or a queen
<u><em>step(ii):-</em></u>
The probability of drawing of a king or a queen from a standard deck of playing cards
P( E₁ U E₂ ) = P(E₁) +P(E₂)

P( E₁ U E₂ ) = 
<u><em>step(iii):-</em></u>
The probability of drawing the compliment of a king or a queen from a standard deck of playing cards



<u><em>Conclusion</em></u>:-
The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846
Answer:
S = {0,2,3,4}
P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001
Mean = 0.879
Standard Deviation = 1.033
Step-by-step explanation:
Let the number of people having same birth month be = x
The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)
The number of ways of distributing their birthdays = 12⁴
The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)
P(X = 0) = 
P(X=0) = 0.573
P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)
P(X=2) = 
P(X=2) = 0.401
P(X=3) = 
P(x=3) = 0.025
P(X=4) = 
P(X=4) = 0.001
Mean, 

Standard deviation, ![SD = \sqrt{\sum x^{2} P(x) - \mu^{2}} \\SD =\sqrt{ [ (0^{2} * 0.573) + (2^{2} * 0.401) + (3^{2} * 0.025) + (4^{2} * 0.001)] - 0.879^{2}}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%5Csum%20x%5E%7B2%7D%20P%28x%29%20-%20%5Cmu%5E%7B2%7D%7D%20%20%5C%5CSD%20%3D%5Csqrt%7B%20%5B%20%280%5E%7B2%7D%20%2A%200.573%29%20%2B%20%282%5E%7B2%7D%20%20%2A%200.401%29%20%2B%20%283%5E%7B2%7D%20%2A%200.025%29%20%2B%20%284%5E%7B2%7D%20%2A%200.001%29%5D%20-%200.879%5E%7B2%7D%7D)
SD = 1.033
Answer:
B. 225 π sq. units
Step-by-step explanation:
the diameter of circle = √18²+24²
=√324+576=√900 = 30
the radius = ½×30=15
the area of circle =
π × 15² = π × 225 = 225 π sq. units
Answer:
m∠ADC = 132°
Step-by-step explanation:
From the figure attached,
By applying sine rule in ΔABD,


sin(∠ADB) = 
= 0.74231
m∠ADB = 
= 47.92°
≈ 48°
m∠ADC + m∠ADB = 180° [Linear pair of angles]
m∠ADC + 48° = 180°
m∠ADC = 180° - 48°
m∠ADC = 132°