Respuesta :
Answer:
The probability that an odd number rolls of a die for less than 3 times is 0.054.
Step-by-step explanation:
The sample space of rolling a fair die is, S = {1, 2, 3, 4, 5, 6}
The odd numbers are, {1, 3, and 5}.
The probability that an odd number occurs is:
[tex]P(Odd)=\frac{Favorable\ outcomes}{Total\ no.\ of\ outcomes}=\frac{3}{6}=\frac{1}{2}[/tex]
The die was rolled n = 10 times.
Let X = number of rolls in which an odd number occurs.
The random variable [tex]X\sim Bin(n=10,p=\frac{1}{2})[/tex]
The probability distribution of binomial is:
[tex]P(X =x)={n\choose x}p^{x}(1-p)^{n-x}[/tex]
Compute the probability that an odd number will occur less than 3 times as follows:
[tex]P(X<3)=P(X=2)+P(X=1)+P(X=0)\\={10\choose 2}(\frac{1}{2} )^{2}(1-\frac{1}{2} )^{10-2}+{10\choose 1}(\frac{1}{2} )^{1}(1-\frac{1}{2} )^{10-1}+{10\choose 0}(\frac{1}{2} )^{0}(1-\frac{1}{2} )^{10-0}\\=0.044+0.009+0.001\\=0.054[/tex]
Thus, the probability that an odd number rolls of a die for less than 3 times is 0.054.
