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SashulF [63]
3 years ago
8

Which is greatest 3/5, 0.70, or 65%? Tell how you know.

Mathematics
1 answer:
Leni [432]3 years ago
8 0
3/5 = .60, 65% = .65, 0.70 is the greatest
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\begin{gathered} P_x=\binom{n}{x}p^xq^{n-x} \\ \text{where} \\ P\text{ is the binomial probability} \\ x\text{ is the number of times for a specific outcome within }n\text{ trials} \\ p\text{ is the probability of success on a single trial} \\ q\text{ is the probability of failure on a single trial} \\ n\text{ is the number of trials} \end{gathered}

Here, we will assume that finding the flaw is the "success" of the trial hence the following given

\begin{gathered} p=0.05 \\ q=0.95 \\ n=30 \end{gathered}

Finding the probability of one flawed scarf

\begin{gathered} P(X=1)=\binom{30}{1}(0.05)^1(0.95)^{30-1} \\ P(X=1)=0.3389 \end{gathered}

Finding the probability of no flawed scarves

\begin{gathered} P(X=0)=\binom{30}{0}(0.05)^0(0.95)^{30-0} \\ P(X=0)=0.2146 \end{gathered}

Finding the probability of more then three flawed scarves

\begin{gathered} P(X>3)=1-P(X\le3) \\ P(X>3)=1-0.93922843869 \\ P(X>3)=0.0608 \end{gathered}

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1 year ago
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