Three students

MATHEMATICS · Single correct · A Level · Mathematics · Probability · Probability

Problem

Three students

S_1, S_2

, and

S_3

are given a problem to solve. Consider the following events: -

U

: At least one of

S_1, S_2

, and

S_3

can solve the problem, -

V

S_1

can solve the problem, given that neither

S_2

nor

S_3

can solve the problem, -

W

S_2

can solve the problem and

S_3

cannot solve the problem, -

T

S_3

can solve the problem. For any event

E

, let

P(E)

denote the probability of

E

. If

P(U) = \frac{1}{2}, \quad P(V) = \frac{1}{10}, \quad \text{and} \quad P(W) = \frac{1}{12},

then

P(T)

is equal to (A)

\frac{13}{36}

(B)

\frac{1}{3}

(C)

\frac{19}{60}

(D)

\frac{1}{4}