Question 1210371
<pre>
I'm thinking that you may have typed 19/70 when it should have been 69/70.

Candidates Q, R, and T are allowed to solve an advanced level Physics question
independently. The probability that Q solves the question is 9/10, R solves the
question is 3/7, and T solves the question is x.
(a) If the probability that at least one candidate solves the question is
{{{cross(19/70)}}} {{{69/70}}}, find the value of x.

The probability that at least one candidate solved it is 1 minus the probability
that no candidate solved it, which is

{{{P(matrix(1,5,Q,does,not,solve,it))}}}{{{""*""}}}{{{P(matrix(1,5,R,does,not,solve,it))}}}{{{""*""}}}{{{P(matrix(1,5,T,does,not,solve,it))}}}{{{""=""}}}
{{{(1-9/10)(1-3/7)(1-x) = expr(1/10)expr(4/7)(1-x) = expr(4/70)(1-x)}}}
This must equal 1-69/70 or 1/70

{{{expr(4/70)(1-x)=1/70}}}
{{{4(1-x)= 1}}}
{{{4-4x=1}}}
{{{-4x=-3}}}
{{{x=3/4}}}  <-- the value of x, which is the probability that T solves it.

>>>(i) At least one candidate solves the question.

Now, I do have to wonder why you asked this, since you gave it as <s>19/70</s> and I 
changed it to 69/70.

The answer, of course is 69/70.  LOL

>>>(ii) At most one candidate solves the question. 

That's the probability that exactly one solved it or exactly none solved it.

case Q R T 
 1   Y N N  (9/10)(1-3/7)(1-3/4) = (9/10)(4/7)(1/4) = 9/70 
 2   N Y N  (1-9/10)(3/7)(1-3/4) = (1/10)(3/7)(1/4) = 3/280
 3   N N Y  (1-9/10)(1-3/7)(3/4) = (1/10)(4/7)(3/4) = 3/70
 4   N N N  (1-9/10)(1-3/7)(1-3/4) = (1/10)(4/7)(1/4) = 1/70

Sum those 4 fractions and get 11/56.

Edwin</pre>