Question

Problem 1 A box has eight balls. There are four green balls and four yellow. The four green balls are numbered 1,2,3, and 4. The four yellow balls are numbered 1,2,3, and 4. The box is shaken. One ball is selected will mean that a green Answer the following questions, using fractions in p/q format or decimal values accurate to the nearest 0.01 .Here G ball is selected, Y that a yellow ball is selected, and E that an even-numbered ball is selected. a. (25%) Select the color/number pairs which comprise the sample space. G1 G2 G3 G4 G5 G6 G7 G8 0 0 0 0 0 0 0 0 2 73 0 74 0 75 0 76 0 77 0 78 0 b. (15%) P(G) = C.(15%) P(GE) - d. (15%) P( G E) = . (15%) PGUE) - (15%) Are G and E mutually exclusive? Dick B

Answer 1

a) G1 G2 G3 G4 Y1 Y2 Y3 Y4 comprise of the same space. (There are no balls numbered with 5 6 7 and 8)

b) P(G)= Probability of the ball being picked is green = 4/8=0.50 (Since 4 out of total 8 balls are green)

c) P(G|E) = Probability of a green ball being picked given that an even number was n=picked= 2/4=0.50 (Since a total of 4 balls are even and 2 out of those are green)

d) P(G and E) = Probability of the ball being picked is Green and even= 2/8=0.25 (Since 2 out of the 8 balls is both green and even G2 and G4)

e) P(G or E) = Probability of the ball being either green or even or both= 6/8=0.75 (Only Y1 and Y3 are excluded out of the 8 balls)

f) Are G and E mutually exclusive? No

G and E being mutually exclusive means both cannot happen at the same time and P(G and E) will be zero, however that is not the case and it is possible for ball to be both green and even at the same time. Hence they are not mutually exclusive.

Hope it helps. Do ask for any clarifications required.