Suppose that in order for the defendant to be convicted in a military court the majority of the nine appointed judges must enter a guilty vote. assume that a judge enters a guilty vote with probability 0.2 or 0.8 if the defendant is innocent or guilty, respectively, independently of other judges. assume also that 50% of the defendants in such trials are innocent.
(a) what proportion of all defendants is convicted?
(b) what is the proportion of correct verdicts?

a) 0.5

b) 0.8

Step-by-step explanation:

Given:

P(Convicted | Innocent) = 0.2

P(Convicted | guilty) = 0.8

P(Innocent) = 50% = 0.5

P(Guilty) = 0.5

a) P(defendant is convicted)

= P(guilty and convicted) + P(innocent and convicted)

= P(Guilty) × P(Convicted | guilty)  +  P(Innocent) × P(Convicted | Innocent)

= 0.5 × 0.8 + 0.5 × 0.2

= 0. 4 + 0.1

= 0.5

b) P(correct verdict)

= P(guilty and convicted) + P(innocent and not convicted)

= P(Guilty) × P(Convicted | guilty) + P(Innocent) × (1 - P(Convicted | Innocent) )

= 0.5 × 0.8 + 0.5 × ( 1 - 0.2)

= 0.4 + 0.4

= 0.8

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

here the number -5 is all of the following except a rational number.

step-by-step explanation: