A random experiment consists of drawing a marble from an urn. There are ten marb

Question

A random experiment consists of drawing a marble from an urn.  There are ten marbles in the urn.  Three are red, and they are numbered 1, 3, and 5.  Four are blue, and they are numbered 3, 4, 5, and 6.  Three are green, and they are numbered 1, 2, and 6.

The probability of drawing a green marble is 0.18 for each of the three green marbles.  The red marble numbered 3 is drawn with probability 0.12, and the blue marble numbered 3 is drawn with probability 0.14.  All other marbles are drawn with probability 0.04.

d) Compute the probability that the marble is blue or numbered 5?

e) Compute the probability that the marble is blue and has an odd number.

f) Compute the probability that the marble is red and has an even number?

g) Compute the probability that the marble is red and has an odd number?

Explanation / Answer

d) Probability that the marble drawn is blue or numbered 5 would be computed as:

= P(blue) + P( 5 red )

= P(3 blue) + P(4 blue) + P(5 blue) + P(6 blue) +P( 5 red )

= 0.14 + 0.04 + 0.04 + 0.04 + 0.04

= 0.3

Therefore 0.3 is the required probability here.

e) Probability that the marble drawn is blue and has an odd number would be computed as:

= P(blue and odd)

= P(3 blue) + P(5 blue)

= 0.14 + 0.04

= 0.18

Therefore 0.18 is the required probability here.

f) Probability that the marble drawn is red and even numbered would be computed as:

= P(red and even)

Now there is no marble which is red and has an even number because all 3 red marbles are odd numbered: 1,3 and 5.

Therefore 0 is the required probability here.

g) Probability that the marble drawn is red and odd numbered would be computed as:

= P(red and odd)

= P( 1 red ) + P(3 red ) + P(5 red )

= 0.04 + 0.12 + 0.04

= 0.2

Therefore 0.2 is the required probability here.

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