Answer:
P(X ≥ 1) = 0.50
Step-by-step explanation:
Given that:
The word "supercalifragilisticexpialidocious" has 34 letters in which 'i' appears 7 times in the word.
Then; the probability of success = 7/34 = 0.20588
Using Binomial distribution to determine the probability; we have:
[tex]P(X = x) = ^nC_x \ \beta^x \ (1 - \beta)^{n-x}[/tex]
where;
x = 0,1,2,...n and 0 < β < 1
and x represents the number of successes.
However; since the letter is drawn thrice; the probability that the letter "i" is drawn at least once can be computed as:
P(X ≥ 1) = 1 - P(X< 1)
P(X ≥ 1) = 1 - P(X =0)
[tex]P(X \ge 1) = 1 - \bigg [ {^3C__0} (0.21)^0 (1-0.21)^{3-0} \bigg][/tex]
[tex]P(X \ge 1) = 1 - \bigg [ 1 \times 1 (0.79)^{3} \bigg][/tex]
P(X ≥ 1) = 1 - 0.50
P(X ≥ 1) = 0.50
