Question

Conditional Probability Two fair dice are rolled: (a) Express the sample space S in set builder notation and the probability P "At least one of the dice rolls a four." Write all possible outcomes of A (b) Consider the event A (c) What is the probability that at least one die rolls a four? (d) What is the conditional probability that the first die rolls a four given that the sum of the dice is six? (e) What is the conditional probability that the first die rolls two or three, given that the sum of the dice is six?

Answer 1

ANSWER:- Given that . Two fair dice are rolled. a) The sample space s in set builder - notation and the probability p. (1,1),(1,2), (1,3), (1.0), (1,5)(1.0), (2,1),(2,1) 1 1913), (2, 4), (2,5), (2.6), (3,1),(3,2),(3,3).(3,4) (3,5),(3;6), (0.1), (,2), (4,3), (uu), (4.5) (urb) (5,1),(5,2), (5,3), (5,4, (5,5), (5,6), (0.1), (2) Y (6.3). 16.0) (6.3). 10,6) or so(alb) lisalbsc]

b) The event A = "At least one of The dice - ralls a four- > Ilu,u),(4.),14,1),(6,4), (5,0) I (n.), (1, u), (2,4),(4,2),(3,4), (,3) ) c) The probability that at least one dide ralls a four SP /E) : ill 36 d) The conditional probability That The first die rolls a tour own & given that the sum of The dice is six- - let B = sum of dice is six = P(B) = 5/26 -|(313), (4,2), (2,4), (5,1),(1,5)}

let ca first dice rolls a your peer- ./10.1),(4,2), (013), (4,4), (us),(40)} Pl%) - Alone P(B) 3 736 5736 -Pleat 451 C) the conditional probability that the first die rolls two or three. >> or first die two or three >> B10 = {(3,3), (2,4)} > P(/) P(02B) PCB 36 /