Answer:
0.70319018
Step-by-step explanation:
Given the following:
Number of students surveyed (n) = 15
Probability of attending tet festival (p) = 24% =0.24
Therefore,
Probability of not attending (1 - p) = (1 - 0.24) = 0.76.
The probability that at most 4 students will attend can be obtained using the binomial probability relation:
p(x) = nCx * p^x * (1 - p)^(n-x)
At most 4 students means:
p(x=0) + p(x=1) + p(x=2) + p(x=3) + p(x=4)
p(x=0) = 15C0 * 0.24^0 * 0.76^(15 - 0)
p(x=0) = 1 * 1 * 0.0004701 = 0.00047018
p(x=1) = 15C1 * 0.24^1 * 0.76^(14)
p(x=1) = 15 * 0.24 * 0.021448 = 0.07721
p(x=2) = 15C2 * 0.24^2 * 0.76^(13) =
p(x=2) = 105 * 0.0576 * 0.02822 = 0.17068
p(x=3) = 15C3 * 0.24^3 * 0.76^(12)
p(x=3) = 455 * 0.013824 * 0.037133 = 0.23356
p(x=4) = 15C4 * 0.24^4 * 0.76^(11) =
p(x=4) = 1365 * 0.0033177 * 0.048859 = 0.22127
0.00047018 + 0.07721 + 0.17068 + 0.23356 + 0.22127 = 0.70319018
