A) \[\frac{1}{9}\]
B) \[\frac{2}{9}\]
C) \[\frac{2}{7}\]
D) None
Correct Answer: A
Solution :
[a] p = P (correct forecasting) \[=\frac{1}{3}\] q = P (wrong forecasting) \[=\frac{2}{3}\] n=4 let r be the number of correct forecast P(At least three correct results). \[=P\left( r=3 \right)+P\left( r=4 \right)\] \[P{{=}^{4}}{{C}_{3}}{{\left( p \right)}^{3}}{{\left( q \right)}^{1}}{{+}^{4}}{{C}_{4}}{{\left( p \right)}^{4}}{{\left( q \right)}^{0}}\] \[P=4{{\left( \frac{1}{3} \right)}^{3}}\left( \frac{2}{3} \right)+{{\left( \frac{1}{3} \right)}^{4}}\] \[={{\left( \frac{1}{3} \right)}^{3}}\left( \frac{8}{3}+\frac{1}{3} \right)\] \[=3\times \frac{1}{27}=\frac{1}{9}\]You need to login to perform this action.
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