probability that both marbles drawn will be white

[chanceandcade]

Suppose a person has four black marbles and two white marbles in one hand, and has six black marbles and five white in the other hand. If he drops one marble from each hand, what is the probability that both marbles will be white?

The answer I get is 7/69 Thanks

 

[soroban]

Re: probability

Hello, chanceandcade!

Of a person has four black marbles and two white marbles in one hand
and six black marbles and five white in the other hand
and drops one marble from each hand,
what is the probability that both marbles will be white?

The answer I get is 7/69 . . . how?

Hand #1 has 6 marbles: 4 Black and 2 White.
Then \(\displaystyle P(\text{White from hand #1}) \:=\:\frac{2}{6}\:=\:\frac{1}{3}\)

Hand #2 has 11 marbles: 6 Black and 5 White.
Then \(\displaystyle P(\text{White from hand #2}) \:=\:\frac{5}{11}\)


Therefore: \(\displaystyle P(\text{White from hand #1 and hand #2}) \:=\:\left(\frac{1}{3}\right)\left(\frac{5}{11}\right)\:=\;\fbox{\frac{5}{33}}\)

 

[marcmtlca]

I would add a small comment as the events being independent which is what allows you to do P( A and B)=P(A)P(B)