An urn contains two red balls and five blue balls a Draw two

An urn contains two red balls and five blue balls.

a.) Draw two balls without replacement, what is the probability that we draw two blue balls?

b.) Draw two balls without replacement, what is the probability that we drat two balls in the same color?

Solution

Whe we draw two balls without replacement it means that we can can do this in:

⁷C₁ X ⁶C₁ = 42 ways

Now we draw two blue balls without replacement in:

⁵C₁ X ⁴C₁ = 20 ways

Thus,

the probability that we draw two blue balls= 20/45= 0.4444

b)

the probability that we draw two balls in the same color would comprise two cases

(A)when both balls are blue= 20/45(Calculated above)

(B) when both balls are red in colour

P(Both balls are red in colour) = ²C₁ X ¹C₁ = 2 ways

the probability that we draw two red balls= 2/45= 0.04444

the probability that we drat two balls in the same color = P(A) + P(B)

0.4444+ 0.04444

= 0.48888