Take another guess: A student takes a multiple-choice test that has 7 questions. Each question has five choices. The student guesses randomly at each answer. Round the answers to three decimal places.
Part 1 of 2
(a) Find $P(4)$.
$$P(4)=$$

Part 2 of 2
(b) Find $P$ (More than 2 ).
$$P(\text{ More than }2)=$$

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Step 1 ：Calculate the combinations for 7 items taken 4 at a time: $C(7,4)=\frac{7!}{4!(7-4)!}=35$

Step 2 ：Calculate the probability of guessing 4 questions correctly: $(1/5{)}^4=0.0016$

Step 3 ：Calculate the probability of guessing the remaining 3 questions incorrectly: $(4/5{)}^3=0.512$

Step 4 ：Multiply these values together to find the probability of guessing exactly 4 questions correctly: $P(4)=35\ast 0.0016\ast 0.512=0.028672$

Step 5 ：$\boxed{{\displaystyle P(4)\approx 0.029}}$ when rounded to three decimal places

Step 6 ：Calculate the combinations and probabilities for guessing exactly 3, 5, 6, and 7 questions correctly in a similar way

Step 7 ：$P(3)=C(7,3)\ast (1/5{)}^3\ast (4/5{)}^4=0.103$

Step 8 ：$P(5)=C(7,5)\ast (1/5{)}^5\ast (4/5{)}^2=0.006$

Step 9 ：$P(6)=C(7,6)\ast (1/5{)}^6\ast (4/5{)}^1=0.001$

Step 10 ：$P(7)=C(7,7)\ast (1/5{)}^7\ast (4/5{)}^0=0.000$

Step 11 ：Add these probabilities together to find the probability of guessing more than 2 questions correctly: $P(\text{ More than }2)=0.103+0.029+0.006+0.001+0.000=0.139$

Step 12 ：$\boxed{{\displaystyle P(\text{ More than }2)\approx 0.139}}$ when rounded to three decimal places