(a) In a bakery, 30% of loaves of bread produced are of bad quality. If twelve loaves are selected at random from the bakery, calculate, correct to four dec...
Question 1 Report
(a) In a bakery, 30% of loaves of bread produced are of bad quality. If twelve loaves are selected at random from the bakery, calculate, correct to four decimal places. the probabshty of getting
(i) exactly 6 bad ones:
(ii) at least 4 bad ones;
(ii) no bad one.
(b) A group consists of 8 boys and 5 girls. A committee of 7 members is chosen from the group. Find the probability that the committee is made up of 4 boys and 3 girls.
Answer Details
(a) \(P(\text{bad})=0.3,\ P(\text{good})=0.7,\ n=12\), \(P(X=r)=\binom{12}{r}(0.3)^r(0.7)^{12-r}\) (\(X\)=number bad).
(i) exactly 6 bad: \(\binom{12}{6}(0.3)^6(0.7)^6=924(0.000729)(0.117649)=0.0793\).
(ii) at least 4 bad \(=1-\big[P(0)+P(1)+P(2)+P(3)\big]\):
\[P(0)=0.0138,\ P(1)=0.0712,\ P(2)=0.1678,\ P(3)=0.2397;\ \text{sum}=0.4925.\] \[P(X\ge 4)=1-0.4925=0.5075.\](iii) no bad one: \(P(0)=(0.7)^{12}=0.0138\).
(b) 8 boys, 5 girls; committee of 7 with 4 boys and 3 girls:
\[P=\frac{\binom{8}{4}\binom{5}{3}}{\binom{13}{7}}=\frac{70\times 10}{1716}=\frac{700}{1716}=\frac{175}{429}\approx 0.4079.\]Download The App On Google Playstore
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