document.write( "Question 1210371: 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.\r
\n" ); document.write( "\n" ); document.write( "(a) If the probability that at least one candidate solves the question is 19/70, find the value of x.\r
\n" ); document.write( "\n" ); document.write( "(b) Find the probability that:
\n" ); document.write( " (i) At least one candidate solves the question.
\n" ); document.write( " (ii) At most one candidate solves the question. \n" ); document.write( "
Algebra.Com's Answer #852113 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "I'm thinking that you may have typed 19/70 when it should have been 69/70.\r\n" );
document.write( "\r\n" );
document.write( "Candidates Q, R, and T are allowed to solve an advanced level Physics question\r\n" );
document.write( "independently. The probability that Q solves the question is 9/10, R solves the\r\n" );
document.write( "question is 3/7, and T solves the question is x.\r\n" );
document.write( "(a) If the probability that at least one candidate solves the question is\r\n" );
document.write( "\"cross%2819%2F70%29\" \"69%2F70\", find the value of x.\r\n" );
document.write( "\r\n" );
document.write( "The probability that at least one candidate solved it is 1 minus the probability\r\n" );
document.write( "that no candidate solved it, which is\r\n" );
document.write( "\r\n" );
document.write( "\"P%28matrix%281%2C5%2CQ%2Cdoes%2Cnot%2Csolve%2Cit%29%29\"\"%22%22%2A%22%22\"\"P%28matrix%281%2C5%2CR%2Cdoes%2Cnot%2Csolve%2Cit%29%29\"\"%22%22%2A%22%22\"\"P%28matrix%281%2C5%2CT%2Cdoes%2Cnot%2Csolve%2Cit%29%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "This must equal 1-69/70 or 1/70\r\n" );
document.write( "\r\n" );
document.write( "\"expr%284%2F70%29%281-x%29=1%2F70\"\r\n" );
document.write( "\"4%281-x%29=+1\"\r\n" );
document.write( "\"4-4x=1\"\r\n" );
document.write( "\"-4x=-3\"\r\n" );
document.write( "\"x=3%2F4\"  <-- the value of x, which is the probability that T solves it.\r\n" );
document.write( "\r\n" );
document.write( ">>>(i) At least one candidate solves the question.\r\n" );
document.write( "\r\n" );
document.write( "Now, I do have to wonder why you asked this, since you gave it as 19/70 and I \r\n" );
document.write( "changed it to 69/70.\r\n" );
document.write( "\r\n" );
document.write( "The answer, of course is 69/70.  LOL\r\n" );
document.write( "\r\n" );
document.write( ">>>(ii) At most one candidate solves the question. \r\n" );
document.write( "\r\n" );
document.write( "That's the probability that exactly one solved it or exactly none solved it.\r\n" );
document.write( "\r\n" );
document.write( "case Q R T \r\n" );
document.write( " 1   Y N N  (9/10)(1-3/7)(1-3/4) = (9/10)(4/7)(1/4) = 9/70 \r\n" );
document.write( " 2   N Y N  (1-9/10)(3/7)(1-3/4) = (1/10)(3/7)(1/4) = 3/280\r\n" );
document.write( " 3   N N Y  (1-9/10)(1-3/7)(3/4) = (1/10)(4/7)(3/4) = 3/70\r\n" );
document.write( " 4   N N N  (1-9/10)(1-3/7)(1-3/4) = (1/10)(4/7)(1/4) = 1/70\r\n" );
document.write( "\r\n" );
document.write( "Sum those 4 fractions and get 11/56.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );