Question 1160920: What is the probability of each student winning the competition if four students, Mary, Alice,Jessy and Simon compete in a mathematical quiz? Mary is three times as likely to win the quiz as Alice. Jessy is twice as likely to win the quiz as Simon. The probability that either Mary or Jessy wins the quiz is 0.7.
Answer by ikleyn(52855)   (Show Source):
You can put this solution on YOUR website! .
I will translate the statement to the Algebra language.
Let M, A, J and S be the corresponding probabilities for each of the participant.
Then from the condition, you have this system of 4 equations
M + A + J + S = 1 (1)
M = 3A (2)
J = 2S (3)
M + J = 0.7 (4)
The translation is just completed.
Note that (4) is true since the events to win for M and for J are DISJOINT.
The rest is just technique, and I do not want to deprive you a joy to complete the solution on your own.
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