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Answer

3/20

Explanation
Probability is a ratio of number of  favourable outcome to the number of total outcome.
In out question, we are going to find the probability of picking a blue ball from each urn.

In urn I
P(b) = 6/(6+4)
        = 6/10
        = 3/5

In urn II
P(b) = 2/(6+2)
        =2/8
        = 1/4

Probability of picking a blue ball from urn I and urn II will be;

3/5 × 1/4 = 3/20
Answer: Fourt option: 3/20

Solution:

Probability that both balls are blue?

Event: Ball drawn from Urn I is blue: A
Event: Ball drawn from Urn II is blue: B

Probability that both balls are blue=Probability that ball drawn from Urn I is blue and ball drawn from Urn II is blue

Probability that both balls are blue = P(A ∩ B)

These events are independent, then:
P(A ∩ B)=P(A) P(B)

P(A)=(Number of blue balls in Urn I)/(Total number of balls in Urn I)
Total number of balls in Urn I=4 green +6 blue=10
P(A)=6/10
Simplifying the fraction: Dividing the numerator and denominator by 2:
P(A)=(6/2)/(10/2)
P(A)=3/5

P(B)=(Number of blue balls in Urn I))/(Total number of balls in Urn II)
Total number of balls in Urn II=6 green +2 blue=8
P(B)=2/8
Simplifying the fraction: Dividing the numerator and denominator by 2:
P(B)=(2/2)/(8/2)
P(B)=1/4

Then:
P(A ∩ B)=P(A) P(B)=(3/5)(1/4)=[(3)(1)] / [(5)(4)]
P(A ∩ B)=3/20

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