Question

Question 3 6 pts A hat contains four red cards numbered 1 through 4; five blue cards numbered 1 through 5; and two green cards numbered 1 and 2, respectively. Find the following probabilities (with replacement). Give your answers as fractions. a. P(Blue) = b. With one draw, P(Blue and Even) = c. With one draw, P(Blue or Even) = d. With one draw, P(Red Even) = e. With one draw, P(Even/Red) = f. With two draws, P(first card Green and second card Even) -

Answer 1

A.

P(Blue) = 5/11

= 0.455

B.

P(Blue and Even) = 2/11

= 0.182

C.

P(Even) = 5/11

= 0.455

P(Blue or even) = P(Blue) + P(Even) - P(Blue and Even)

=0.455+0.455-0.182

= 0.728

D.

P(Red and Even) = 2/11

= 0.182

P(Red|Eeven) = P(Red and Even)/P(Even)

= 0.182/0.455

= 0.4

E.

P(Red) = 4/11

= 0.364

P(Even|Red) = P(Red and Even)/P(Red)

= 0.182/0.364

= 0.5

G.

P(First Card Green and second card even) = P(First Card Green and second card even|First green card is odd) + P(First Card Green and second card even|First green card is even)

= 2/11*5/11*1/2 + 2/11*4/11*1/2

= 0.0744

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