The probability that a student at a large music college plays in the band is $$\(0.6\)$$. For a student who plays in the band, the probability that she also sings in the choir is $$\(0.3\)$$. For a student who does not play in the band, the probability that she sings in the choir is $$\(x\)$$. The probability that a randomly chosen student from the college does not sing in the choir is $$\(0.58\)$$. Find the value of $$\(x\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_51 Year：2020 Question No：2(a)
Answer:
\( \begin{array}{l}
0 \cdot 6 \times 0 \cdot 7+0 \cdot 4(1-x)=0 \cdot 58
\equiv 0 \cdot 42+0 \cdot 4(1-x)=0 \cdot 58
\end{array}
\)
\( x=0 \cdot 6
\)
Alternative method for question 2(a)
\( \begin{array}{l}
0 \cdot 6 \times 0 \cdot 3+0 \cdot 4 x=0 \cdot 42
\equiv 0 \cdot 18+0 \cdot 4 x=0.42
\end{array}
\)
\( x=0 \cdot 6
\)
0 \cdot 6 \times 0 \cdot 7+0 \cdot 4(1-x)=0 \cdot 58
\equiv 0 \cdot 42+0 \cdot 4(1-x)=0 \cdot 58
\end{array}
\)
\( x=0 \cdot 6
\)
Alternative method for question 2(a)
\( \begin{array}{l}
0 \cdot 6 \times 0 \cdot 3+0 \cdot 4 x=0 \cdot 42
\equiv 0 \cdot 18+0 \cdot 4 x=0.42
\end{array}
\)
\( x=0 \cdot 6
\)
Knowledge points:
5.3.2 use addition and multiplication of probabilities, as appropriate, in simple cases (Explicit use of the general formula is not required.)
5.3.4 calculate and use conditional probabilities in simple cases.
Solution:
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