Question

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

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