Answer
a) 0.0081
b) MMXX, MXMX, MXXM, XMXM,XMMX, XXMM, 0.0081.
c)0.0486
Work Step by Step
a) The probability of guessing a number correctly is $\frac{1}{10}$ and of gussing incorrectly is $\frac{9}{10}$. ALso, these selections are independent. Therefore the probability:$P(MMXX)=\frac{1}{10}\cdot \frac{1}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}=0.0081.$
b) The good possibilities are MMXX, MXMX, MXXM, XMXM,XMMX, XXMM and each of them have the same probability of 0.0081.
c) Using b), the probability of getting exactly 2 matching digits out of 4 is $6\cdot 0.0081=0.0486$.
