can you answer the questions in the picture. 11. (4 pts) Use the Venn diagram to

Question

can you answer the questions in the picture.

11. (4 pts) Use the Venn diagram to help work this problem. Suppose P(E)=0.26, P(F) =0.41, @t{)..2 12. (3 pts) A marble is drawn from a box containing 3 yellow, 4 white, and 11 blue marbles. Find the odds in favor of drawing the following. Note: The odds in favor of an event E are defined as the ratio of P(E) to P(E) a) a yellow marble to 11o b) a blue marbleo7 c) a white marble to d)not drawing a white marble tto (4 to otl7ts2 13. (2 pts) An experiment is conducted for which the sample space is Is the following probability assignment possible for this experiment? If the assignment is not possible, tell why S (S1, S2, S3, S4, Ss 60-72 > Outcomes S 2 S3 4 S5 Probabilities | ¼ 1/10 1 ,sareehetna^ 0551.ble Girce Page 5 of

Explanation / Answer

11) here P(E1)=1-P(E) =1-0.26=0.74

P(F1)=1-P(F) =1-0.41 =0.59

and P(E1nF1)=1 -P(EnF) =1-(P(E)+P(F)-P(EnF)) =1-(0.26+0.41-0.16)=0.49

hence P(E1UF1)=P(E1)+P(F1)-P(E1nF1) =0.74+0.59-0.49=0.84

(Note this can be solved also by P(E1UF1)=1-P(EnF) =1-0.16 =0.84)

12)

a) a yellow marble =favourable event/unfavourable evemt =3/(4+11) =3/15 =1/5 ; 1to 5

b) blue marble =11/(3+4) =11/7 ;11 to 7

c) white marble =4/(3+11) =4/14 =2/7 ; 2 to 7

d) not draeing a white marble =1/drawing white marble =1/(2/7) =7/2 ; 7 to 2

13)

as for probability distirbution sum of probability should be equal to 1. Also each event probability should lie between 0 and 1( inclusive)

as sum of probability =(1/5+1/3+1/4+1/5+1/10) =(12+20+15+12+6)/60 =65/60=13/12

as sum of probability is greater then 1; it can not be a valid probability distirbution

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