Question

2.  A box has 20 blocks in it.  The blocks are 3 red squares, 2 red circles, 2 red stars, 2 blue squares, 5 blue circles, and 6 blue stars.  For the experiment of pulling a block out at random from the box, first write out the table of joint probabilities for shape and color, and then find the probability of

(a) pulling a red block

(b) pulling a circle

(c) pulling a red block given that you pulled a circle

(d) pulling a circle given that you pulled a red block

(e) pulling a block that is not a star given that it is a blue block

(f) pulling a circle or a star given that you pulled a red block

Answer 1

a) Probability of pulling a red block

= (3 + 2 + 2)/20

= 7/20 = 0.35

Therefore 0.35 is the required probability here.

b) The probability here is computed as:

= (Total circles )/20

= (2 + 5)/20

= 0.35

Therefore 0.35 is the required probability here.

c) Given that a circle is drawn, probability that it was red

P(R | Circle) = Number of red circles / Total number of circles = 2/7

Therefore 2/7 is the required probability here.

d) P( circle | red ) = Total red circles / Total red = 2/7

Therefore 2/7 is the required probability here.

e) P( not a star | blue ) = 5/11

Therefore 5/11 is the required probability here.

f) P( circle or star | red ) = (2 + 2)/7 = 4/7

Therefore 4/7 is the required probability here.