Check the solution to "a) Probability for two or fewer students would..."

sjeikdom0

Answered question

2021-09-19

a) Probability for two or fewer students would win a prize if companys

Neelam Wainwright

Skilled2021-09-20Added 102 answers

a) Calculations:
According to the binomial probability,

P (X = k) = (b e g \in {a r r a y} {c} n ∖ k e n d {a r r a y}) \cdot p^{k} \cdot {(1 - p)}^{n - k}

Addition rule for mutually exclusive event:

P (A \cup B) = P (A or B) = P (A) + P (B)

k = 0

,
The binomial probability to be evaluated as:

P (X = 0) = (b e g \in {a r r a y} {c} 30 ∖ 0 e n d {a r r a y}) \cdot {(0.44)}^{0} \cdot {(1 - 0.44)}^{30 - 0}

= \frac{30!}{0! (30 - 0)!} \cdot {(0.44)}^{0} \cdot {(0.56)}^{30}

= 1 \cdot {(0.44)}^{0} \cdot {(0.56)}^{30}

\approx 0.0042

k = 1

,
The binomial probability to be evaluated as:

P (X = 1) = (b e g \in {a r r a y} {c} 30 ∖ 1 e n d {a r r a y}) \cdot {(0.44)}^{1} \cdot {(1 - 0.44)}^{30 - 1}

= \frac{30!}{1! (30 - 1)!} \cdot {(0.44)}^{1} \cdot {(0.56)}^{29}

= 30 \cdot {(0.44)}^{1} \cdot {(0.56)}^{29}

\approx 0.0253

k = 2

,
The binomial probability to be evaluated as:

P (X = 2) = (b e g \in {a r r a y} {c} 30 ∖ 2 e n d {a r r a y}) \cdot {(0.44)}^{2} \cdot {(1 - 0.44)}^{30 - 2}

= \frac{30!}{2! (30 - 2)!} \cdot {(0.44)}^{2} \cdot {(0.56)}^{28}

= 435 \cdot {(0.44)}^{2} \cdot {(0.56)}^{28}

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