Question

Two five sided dies with numbers 1, 2, 3, 4 and 5 are rolled. There are 25 outcome such as 1,2; 2,3 etc. Let X be the sum o balls. Construct the probability distribution of X. P(x) т 2 3 4 5 6 7 8 9 10 Total 1 Find the probability P( X4)

let the X be the sum of these two balls. construct the probablility distribution of X. (some answrs have 4 decimals, put 0 before the decimal as in 0.325)

Answer 1

solution dies with numbers rolled sample Two five sided 1,2,3,4,5 space (4,1),(1,2) (1,4),(1,4), (1,5),(2,4),(2,2), (2,3),(2,4)(2,5),(3,1),(3, 2), (3,1),(3,4),(3,5), (4;4),(4,2),(4,3),(4,4),(4,5),(5,1),(5,2) (593), (5,4), 6,5) Total no. of outcomes = 25 P/X=2] = Prob Prob of event (1,1) I יו = 0.04 25 X =3 it can occur in two ways either (2, 1) and (2, 2) of favourable outcomes outcome no. Hence plx=3] no. of total 2 = 0.08 25 three X=4 can occur in way (2, 3) (2, 2) and (3,1) Hence P(x=4 no. of favourable outcomes no. of total outcomes 3 25 = 0.12 = X=5 can occur in four ways (1,4),(2,3), (2, 2) and (4,1)

Hence Plx=5] 4 = = 0.16 25 can occur in five ways ( 1,5),(2,4), X=6 (4,2), (3,3), (5,1) P/x=6) 5 25 = 0.2 • X=7 can in four ways (2,5),(3,4),(4,3) (5,2) 4 = 0.16 25 X=8 can occur in 3 = 0.12 25 x=9 can in elx=7] = three ways (3,5), (4,4) (5,3) P(x=8] two ways (5,4),(4,5) p/x=9] = 2 in only one way (5,5) P(x= 10) = 245 the probe of X = 0.08 25 one X=10 can accur = 0.04 Hence distribution 2 3 4 S. 6 7 8 9 10 Plu) 0.04 0.08 0.12 0.16 0.20 0.16 0.12 0.08 0.94