We use the formula for Binomial Probabilities "P_n(k)=C_n^k p^k q^{n-k}"
p=0,05
q=1-p=1-0,05=0,95
n=10
"k \\leqslant 2"
"P_{10}(k\\leqslant 2)=P_{10}(k=0)+P_{10}(k=1)+P_{10}(k=2)"
"P_{10}(k=0)=C_{10}^0 (0.05)^0 (0.95)^ {5-0}=0,5987"
"P_{10}(k=1)=C_{10}^1 (0.05)^1 (0.95)^ {5-1}=0,3151"
"P_{10}(k=2)=C_{10}^2 (0.05)^2 (0.95)^ {5-2}=0,0746"
the probability of at most 2 out of 10 kids getting A grade in that paper is equal to
"P_{10}(k\\leqslant 2)=0,5987+0,3151+0,0746=0,9884"
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