Answer: 0.99483
Step-by-step explanation:
Given : A box contains four 40-W bulbs, five 60-W bulbs, and six 75-W bulbs.
Total bulbs : 4+5+6=15
The probability of selecting a 75-W bulb :[tex]p=\dfrac{6}{15}=0.4[/tex]
Using the binomial probability :-
[tex]P(X)= ^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , p is the probability of getting success in each trial and n is the total number of trials.
We have,
The probability that at least two bulbs must be selected to obtain one that is rated 75W :-
[tex]P(x\geq2)=1-(P(x<2))\\\\=1-(P(x=0)+P(x=1))\\\\=1-(^{15}C_0(0.4)^0(0.6)^{15}+^{15}C_{1}(0.4)^1(0.6)^{14})\\\\=1-((1)(0.6)^{15}+(15)(0.4)(0.6)^{14})\ \ [\because\ ^nC_0=1\ \&\ ^nC_1=n]\\\\\approx1-(0.00047+0.00470)\\\\=1-0.00517=0.99483[/tex]
Hence, the required probability = 0.99483
