Question

Statistics Probability

Answer 1

Answer:

Explained below.

Step-by-step explanation:

Denote the variable as follows:

M = male student

F = female student

Y = ate breakfast

N = did not ate breakfast

(a)

Compute the probability that a randomly selected student ate breakfast as follows:

$P(Y)=\frac{n(Y)}{N}\\\\=\frac{198}{330}\\\\=0.60$

(b)

Compute the probability that a randomly selected student is female and ate breakfast as follows:

$P(F\cap Y)=\frac{n(F\cap Y)}{N}\\\\=\frac{121}{330}\\\\=0.367$

(c)

Compute the probability a randomly selected student is male, given that the student ate breakfast as follows:

$P(M|Y)=\frac{n(M\cap Y)}{n(Y)}\\\\=\frac{77}{198}\\\\=0.389$

(d)

Compute the probability that a randomly selected student ate breakfast, given that the student is male as follows:

$P(Y|M)=\frac{n(Y\cap M)}{n(M)}\\\\=\frac{77}{154}\\\\=0.50$

(e)

Compute probability of the student selected "is male" or "did not eat breakfast" as follows:

$P(M\cup N)=P(M)+P(N)-P(M\cap N)\\\\=\frac{n(M)}{N}+\frac{n(N)}{N}-\frac{n(M\cap N)}{N}\\\\=\frac{n(M)-n(N)-n(M\cap N)}{N}\\\\=\frac{154+132-77}{330}\\\\=0.633$

(f)

Compute the probability of "is male and did not eat breakfast as follows:

$P(M\cap N)=\frac{n(M\cap N)}{N}\\\\=\frac{77}{330}\\\\=0.233$