Answer: 0.726
Step-by-step explanation:
This will be solved by the probability distribution formula for random variables where combination formula for selection is used.
When determining the probability of random variable X, and when X=r,then
P(X=r) = nCr × p^r × q^n-r
Where n = number of sample And in this case, n = 25
r = desired outcome of sample
p = probability of having a successful outcome. And In this Case, p=25%= 0.25
q = 1-p=1-0.25=0.75
To get probability of at most 7 of the samples being fax, we vary the value of x from 0 to 7 And sum up the different values of probability gotten.
When x = 0
P(X=0) = 25C0 × 0.25^0 × 0.75^25 =0.00075
When x=1
P(X=1) = 25C1 × 0.25¹ × 0.75^24 = 0.00627
When x=2
P(X=2) = 25C2 × 0.25² × 0.75^23 = 0.0251
When x=3
P(X=3) = 25C3 × 0.25³ × 0.75^22 = 0.0641
When x = 4
P(X=4) = 25C4 × 0.25^4 × 0.75^21 =0.1175
When x=5
P(X=5) = 25C5 × 0.25^5 × 0.75^20 = 0.1645
When x=6
P(X=6) = 25C6 × 0.25^6 × 0.75^19 = 0.1828
When x=7
P(X=7) = 25C7 × 0.25^7 × 0.75^18 = 0.1654
Hence, P(X≤7) = 0.00075 + 0.00627 + 0.0251 + 0.0641 + 0.1175 + 0.1645 + 0.1828 + 0.1654 = 0.726(3dp)
