Nana adalah consumer loan officer di Bank Mandiri. Berdasarkan pengalamannya, dia memperkirakan peluang seorang nasabah akan mampu membayar hutangnya adalah $0.30$ . Bulan lalu Nana berhasil mendapatkan $20$ nasabah baru. Berapakah peluang paling tidak tiga nasabah bisa membayar hutangnya ? $\newline$ Select one: $\newline$ a. $0.0355$ $\newline$ b. $0.9646$ $\newline$ c. $0.8866$ $\newline$ d. $0.9829$ $\newline$ e. $0.0183$

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Q. Nana adalah consumer loan officer di Bank Mandiri. Berdasarkan pengalamannya, dia memperkirakan peluang seorang nasabah akan mampu membayar hutangnya adalah

0.30

. Bulan lalu Nana berhasil mendapatkan

20

nasabah baru. Berapakah peluang paling tidak tiga nasabah bisa membayar hutangnya ?

\newline

Select one:

\newline

0.0355

\newline

0.9646

\newline

0.8866

\newline

0.9829

\newline

0.0183

Calculate Probability Complement: Calculate the probability that exactly $0$ , $1$ , or $2$ customers will be able to pay back their loans. This is the complement of at least $3$ customers paying back.
Use Binomial Probability Formula: Use the binomial probability formula $P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}$ , where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success, and $\binom{n}{k}$ is the binomial coefficient.
Calculate Probability for $0$ Successes: Calculate the probability for $0$ successes: $P(X=0) = \binom{20}{0} \times 0.30^0 \times (1-0.30)^{20}$ .
Perform Calculation for $0$ Successes: Perform the calculation: $P(X=0) = 1 \times 1 \times 0.7^{20}$ .
Calculate $P(X=0)$ : Calculate $P(X=0)$ : $P(X=0) = 0.7^{20} = 0.000797922$ .
Calculate Probability for $1$ Success: Calculate the probability for $1$ success: $P(X=1) = \binom{20}{1} \times 0.30^1 \times (1-0.30)^{19}$ .
Perform Calculation for $1$ Success: Perform the calculation: $P(X=1) = 20 \times 0.30 \times 0.7^{19}$ .
Calculate $P(X=1)$ : Calculate $P(X=1)$ : $P(X=1) = 20 \times 0.30 \times 0.7^{19} = 0.006839337$ .
Calculate Probability for $2$ Successes: Calculate the probability for $2$ successes: $P(X=2) = \binom{20}{2} \times 0.30^2 \times (1-0.30)^{18}$ .
Perform Calculation for $2$ Successes: Perform the calculation: $P(X=2) = 190 \times 0.30^2 \times 0.7^{18}$ .
Calculate $P(X=2)$ : Calculate $P(X=2)$ : $P(X=2) = 190 \times 0.09 \times 0.7^{18} = 0.040177656$ .
Add Probabilities of $0$ , $1$ , $2$ Successes: Add up the probabilities of $0$ , $1$ , and $2$ successes to find the total probability of these events: $P(X=0) + P(X=1) + P(X=2)$ .
Perform Addition for Total Probability: Perform the addition: Total probability = $0.000797922 + 0.006839337 + 0.040177656$ .
Calculate Total Probability: Calculate the total probability: Total probability = $0.047814915$ .
Subtract from $1$ for at least $3$ Successes: Subtract the total probability from $1$ to find the probability of at least $3$ successes: $1 - \text{Total probability}.$
Perform Subtraction: Perform the subtraction: Probability at least $3 = 1 - 0.047814915$ .