Let X be a sum of results when rolling die twice. P(X at most 5)=

Step-by-step explanation:

A dice has 6 outcomes, S = [1, 2, 3, 4, 5, 6}

When two dice are rolled, the no of outcomes n (S) = 6 * 6 = 36

S = { (1, 1), (1, 2) (1, 6)

       (2, 1)(2, 6)

        (6,6) }

Le X be the event that sum of two dice when rolled is at most 5

At most refers to lesser than or equal to,

Therefore the outcomes for event X = { (1, 1) , (1, 2) , (1, 3) , (1, 4) , (2, 1) , (2, 2) , (2, 3) , (3, 1) , (3, 2) , (4 , 1) }

n (X) = 10

P (X) = n (X) / n (S)

= 10 / 36 = 5 / 18

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°