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: Convert scientific notation to decimals

$2.86 \times 10^{-5} = 0.0000286$
$9.54 \times 10^{-7} = 0.000000954$

Step2: Sum all relevant probabilities

$0.0031 + 0.000386 + 0.0000286 + 0.000000954$

Step3: Calculate total probability

$0.0031 + 0.000386 = 0.003486$
$0.003486 + 0.0000286 = 0.0035146$
$0.0035146 + 0.000000954 = 0.003515554$

Step4: Round to match options

Round $0.003515554$ to 4 decimal places: $0.0035$

Answer:

0.0035