Question

If the probability of a problem being solved by two students is 1/2 and 1/3, respectively, then the probability of that problem being solved is​

Answer 1

$let \: p(a) = \frac{1}{2} \\and \: p(b) = \frac{1}{3}$

$prob.that \: (a) \: solves \: or \: (b) \: solves \\ = p(a \:u \: b)$

= P(A) +P(B) -P(A intersection B)

since a and b are independent

therefore,

P(A intersection B) =

$\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

now apply the given formula which is underlined

$\frac{1}{2} + \frac{1}{3} - \frac{1}{6} \\ \\ \frac{3}{2} + \frac{2}{6} - \frac{1}{6} \\ \\ = \frac{4}{6} \\ = \frac{2}{3}$

I hope it helps you