Jack tosses a fair coin 6 times. Then Jill tosses the same coin 9 times. Write out an expression for the chance that "Jack gets 2 heads and Jill gets 4 heads."
I know that you use the binomial formula to get the chances for each but do you then multiply them together since it's asking for the chance of both or do you just add them?
Hint. The two events are independant, so you can multiply the two probabilities: $$P(A\cap B)=P(A)\times P(B)=\binom{6}{2} 0.5^2\:0.5^4\times\binom{9}{4}0.5^4\:0.5^5 \approx 0.0577$$
You multiply them, since it's asking for the chance of both. The probability of two events happening is the product of its individual probabilities.
You must multiply the single probabilities.
i.e., if I toss a fair coin I have $p_1 = .5$ of obtain head. In a second toss the probability $p_2 = p_1$ is the same, but the probability that obtain head in each tosses is $p_{1,2} = p_1 \cdot p_2 = .25$ and not $p_{1,2} = p_1 + p_2 = 1$.
