Question

Suppose that you flip five fair coins and roll three fair dices at the same time and all the events are independent. (a) What is the probability that exactly two coins land heads up and one dice shows a six? (b) What is the probability that at least four coins land heads up and two dices show a number less than three? (c) What is the probability that the total number of heads is an even-number and the addition of dices face values equal to less than 6?

Answer 1

Ans. Probability of head = { = p ; failure, q= wis Probability of exactly two heade and - S ujs = Hy probability of exactly one dice showing a six. 32 YA total probability of both at 78 a time = (6 lisat least 4 heads = Suw +6(1)(1) - 6 is at least two dice showing a no less than $3:- Probability of no. less than 3, þ= 2 = 1 - at least two dio a 3,LI? - = 4 + 1/4 = 2 / 2 for both at a time = 6 x I= o.os Channed with CamScanner 39

3 + Tot 5 - 15 1 32 3§ 32 He is probability that noi of head is even Son (W² ( 4 ) ² + sc. 4 W - 10 + 50 - 12 (1) no. of cases having sum less than 6:.. U9;t !! ); (1, 1, 3); (1,3,1);(3,1,1); ('3.'),(3,!) 21 2,2 (2,13 ) (2,2,1) > baobability = g h 16 probability of both at a time - 15 x 10 = o.ag 32 g 36 Liscanned with CamScanner