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: probability of getting exactly 7 correct = 0.0031, probability of getting exactly 8 correct = 0.000386, probability of getting exactly 9 correct = 2.86×10^(-5), probability of 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: Identify passing - conditions

Peter needs at least 7 correct answers. So we need to sum probabilities of getting 7, 8, 9, and 10 correct.

Step2: Sum the probabilities

$P(\text{pass})=P(7)+P(8)+P(9)+P(10)$
$P(7) = 0.0031$, $P(8)=0.000388$, $P(9)=2.86\times 10^{-5}$, $P(10)=9.54\times 10^{-7}$
$P(\text{pass})=0.0031 + 0.000388+2.86\times 10^{-5}+9.54\times 10^{-7}$
$P(\text{pass})=0.0031 + 0.000388+0.0000286 + 0.000000954$
$P(\text{pass})=0.003517554\approx0.0035$

Answer:

0.0035