peter guesses on all 10 questions of a multiple - choice quiz. each question has 4 answer choices, and peter…

peter guesses on all 10 questions of a multiple - choice quiz. each question has 4 answer choices, and peter needs to get at least 7 questions correct to pass. here are some probabilities computed using the binomial formula: p(getting exactly 7 correct)=0.0031, p(getting exactly 8 correct)=0.000386, p(getting exactly 9 correct)=2.86×10^(-5), p(getting exactly 10 correct)=9.54×10^(-7). using the information on the left, combine the individual probabilities to compute the probability that peter will pass the quiz. 0.001, 0.002, 0.0035, 0.005, done

peter guesses on all 10 questions of a multiple - choice quiz. each question has 4 answer choices, and peter needs to get at least 7 questions correct to pass. here are some probabilities computed using the binomial formula: p(getting exactly 7 correct)=0.0031, p(getting exactly 8 correct)=0.000386, p(getting exactly 9 correct)=2.86×10^(-5), p(getting exactly 10 correct)=9.54×10^(-7). using the information on the left, combine the individual probabilities to compute the probability that peter will pass the quiz. 0.001, 0.002, 0.0035, 0.005, done

Answer

Explanation:

Step1: Define passing condition

Peter passes if he gets 7, 8, 9 or 10 questions correct.

Step2: Use probability addition rule

The probability of passing is the sum of the probabilities of getting exactly 7, 8, 9 and 10 questions correct. $P(\text{pass})=P(7)+P(8)+P(9)+P(10)$

Step3: Substitute given probabilities

$P(7) = 0.0031$, $P(8)=0.000386$, $P(9)=2.86\times 10^{-5}=0.0000286$, $P(10)=9.54\times 10^{-7}=0.000000954$ $P(\text{pass})=0.0031 + 0.000386+0.0000286 + 0.000000954$

Step4: Calculate the sum

$P(\text{pass})=0.003515554\approx0.0035$

Answer:

0.0035