Question

22. The sample space of equally likely outcomes for the experiment of rolling two fair dice is 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 61 62 63 64 65 66 Identify the events N: the sum is at least nine. T: at least one of the dice is a two, and Fat least one of the dice is a five. a. Find N). b. Find PNF) c. Find (NIT). d. Determine from the previous answers whether or not the events N and F are independent whether or not N and T are.

Answer 1

Answer & -> The Outcomes Griven that Comple space of equality likely for the exporremont of rolling two 15 ia 23 43 53 si 32 33 34 4, 42 43 51 52 53 61 62 63 64 (a) finding p(a) Given that Ni the Sun af is at least nine Therefore we can get 9 out of 36 cuf Gomes yelling a son of a on gocal er. Then the probability p(N) is ( 36, 45.46,54, 55, 56,63,64, 65,66 )

IO 36 - P(n) = 1 1 0(2) Opava slice (6) Fored on Pawlf) I Gion that Fiat least one of the dire sa five 16, we will get 1l cetcomes were alleast one of the clice asis 25, 35. ur, 5 2 , 53, 54, 5556,65 PCA) = 6 - Gion that 1-) NDF = 45.54 155 156.65 (s cutcome u 36 elemente) plodnf ) : 5/6 Lot (Wils). TP(NIF)= Spore //

(c) (NIT) Given that T: at least one of the live is a two" (12,21,22,23,24, 25, 26, 32,42,52,629 1 cutcomes m 36 cloments (T) = "136 =) NAT = 0 There dove p (Not) = 0 Jn7 to Then (NIT) = P(NOT) P (T) 36 TP(NIT)= 0 / (d) Giora that hallare o are not the events N and are acoperdont wherthore or are not and T croe. F a

36 :-) P(Not) = p (91) *P(1) 648 & nl acord T h osoola Therefore proe not nl and f conclopendent.