Roll two dice, one white and one red. Consider these events: A : The sum is 7 B : The white die is odd C : The red die has a larger number showing than the white D : The dice match (doubles) Which pair(s) of events are disjoint (events A and B are disjoint if A ∩ B = ∅ )? Which pair(s) are independent? Which pair(s) are neither disjoint nor independent?

Step-by-step explanation:

Roll two dice, one white and one red

A = The sum of 7 = [ (3,4),(4,3),(2,5),(5,2),(6,1),(1,6)]

B = the white die is odd = [(1,1),(1,3),(1,5),(2,1),(2,3),(2,5),(6,1),(6,3),(6,5),(3,1),(3,3),(3,5),(4,1),(4,3),(4,5),(5,1),(5,3),(5,5)]

C = Red die has larger number ; [(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)]

a) AnC = ∅  disjoint

b) P(A) = 1/6, P(B) =1/2, P(C) = 1/6

P(AnB) = 1/12, P(AnC) =1/36, P(BnC) = 1/12

A and B, B and C are independent

step-by-step explanation:

it's is b

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°