Answer:
[tex]P(M4\ n\ V) = 2.083\%[/tex]
Step-by-step explanation:
Given
Paper = 20 slips
Word: PENNSYLVANIA
Required
Determine P(Multiple of 4 and V)
The sample size of the 20 slips is:
[tex]n(S) = 20[/tex]
The outcomes of multiples of 4 is:
[tex]M4= \{4,8,12,16,20\}[/tex]
[tex]n(M4) = 5[/tex]
So, the probability of multiples of 4 is:
[tex]Pr(M4) = \frac{5}{20}[/tex]
[tex]Pr(M4) = \frac{1}{4}[/tex]
The sample size of PENNSYLVANIA is:
[tex]n(S) = 12[/tex]
The outcome of V is:
[tex]n(V) = 1[/tex]
So, the probability of V is:
[tex]P(V) = \frac{1}{12}[/tex]
So, the required probability is: P(Multiple of 4 and V)
[tex]P(M4\ n\ V) = P(M4) * P(V)[/tex]
[tex]P(M4\ n\ V) = \frac{1}{4} * \frac{1}{12}[/tex]
[tex]P(M4\ n\ V) = \frac{1}{48}[/tex]
[tex]P(M4\ n\ V) = 0.02083[/tex]
Express as percentage
[tex]P(M4\ n\ V) = 0.02083 * 100\%[/tex]
[tex]P(M4\ n\ V) = 2.083\%[/tex]
