Consider independently rolling two fair dice, one red and the other green. let a be the event that the red die shows 3 dots, b be the event that the green die shows 4 dots, and c be the event that the total number of dots showing on the two dice is 7. are these events pairwise independent (i. e., are a and b independent events, are a and c independent, and are b and c independent)? yes, the events are pairwise independent. no, one pair is not independent. no, two pairs are not independent. no, none of the pairs are independent. are the three events mutually independent? yes, the three events are mutually independent. no, the three events are not mutually independent.

(a). No, two pairs are not independent.

(b). No, the three events are not mutually independent.

Step-by-step explanation:

The events are said to be independent event if occurrence of one event does not affect the other event.

(a) The event A and B are independent to each other, Since occurrence of one event does not affect the other event.

But event (A and C) and event (B and C) are dependent event. Since occurring of event C is depend on the events A and B.

Thus, two pairs are not independent.

(b) Since occurring of event C is depend on the events A and B. Thus, the three events are not mutually independent.

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9