Holly takos a 25 question multiple choice exam wech quention has four ponmible a

Question

Holly takos a 25 question multiple choice exam wech quention has four ponmible answers. Some of the answers .he known·arid sorne she erts nght by s the probability of her knowing the answer to a randomly selected question siven that she got it right is 0.95 How many of the 25 questions was she prepared for Justify your answer 5. A die is tossed. If a number less than 3 turns up, then two coins are lipped, Otherwise, three coins are tossed. What is the probability that two heads turn up Justify your answer 6. Two fair dice are rolled, what is the probability that that the number showing on one will be twice the number appearing on the other. Justify your answer. 7. In how many ways can the letters of "newjerseysouth" be arranged so that r is preceded by an n and followed by an e? Justify your answer 8. Five fair dice are rolled. What is the probability that the faces showing constitute a "full house": three of the faces show one number and the other two faces show a different number. Justify your answer Is it more 9. A computer has generated seven random numbers over the interval 0 to 1 likely that (a) exactly three will be in the interval ,1] or (b) fewer than three will greater than Explain. olly pulls two socks out of a drawer er contains 3 red, 5 bla and 6 blue socks, all randomly arranged. What is the probability that the two t are a match? Frttn Crnditi Hour mnnt urars can the letters in the word slumgullion be arranged

Explanation / Answer

Ans:

6)

Favourable outcomes={(1,2),(2,1),(2,4),(4,2),(3,6),(6,3)}

number of favourable outcomes=6

Total possible outcomes=36

Probability the number on one dice will be double the other=6/36=1/6

5)if two coins are tossed,

As,S={HH,TH,HT,TT}

then probability of two heads=1/4

if 3 coins are tossed,then probability of 2 heads=3/8

(S={HHH,HHT,HTH,THH,TTH,THT,HTT,TTT}

Probability of coming up with number less than 3=2/6

Probabilty of coming up with numbre>=3=4/6

P(2 heads)=(1/4)*(2/6)+(3/8)*(4/6)=(2/24)+(12/48)=(1/12)+(1/4)=4/12=1/3

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

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