Answer: 0.6563
Step-by-step explanation:
Given: The probability that adult workers have a high school diploma : p= 0.50
Sample size : n= 6
Let x be the number of workers have high school diploma.
Binomial distribution formula,
[tex]P(X=x)=\ ^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that 3 or more of them have a high school diploma will be:
[tex]P(X\geq3)=1-P(X<2)\\\\=1-(P(X=0)+P(X=1)+P(X=2))\\\\=1-(^6C_0(0.5)^6(1-0.5)^0+^6C_1(0.5)^1(1-0.5)^5+^6C_2(0.5)^2(1-0.5)^4)\\\\=1-((1)(0.5)^6+(6(0.5)(0.5)^5)+\dfrac{6!}{2!4!}(0.5)^2(0.5)^4)\\\\=1-(0.015625+0.09375+0.234375)\\\\=1-0.34375\\\\=0.65625\approx0.6563[/tex]
Hence, required probability = 0.6563
