Respuesta :
Number of questions = 10
Probability of getting correct = 0.5 (because it is a true - false answer)
40% of 10 question = 4 questions
Find P( ≥ 4 questions correct ):
[tex] \text {Probability of getting 4 correct = }\left(\begin{array}{c}10\\4\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{210}{1024} [/tex]
[tex] \text {Probability of getting 5 correct = }\left(\begin{array}{c}10\\5\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{252}{1024} [/tex]
[tex] \text {Probability of getting 6 correct = }\left(\begin{array}{c}10\\6\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{210}{1024} [/tex]
[tex]\text {Probability of getting 7 correct = }\left(\begin{array}{c}10\\7\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{120}{1024} [/tex]
[tex]\text {Probability of getting 8 correct = }\left(\begin{array}{c}10\\8\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{45}{1024} [/tex]
[tex]\text {Probability of getting 9 correct = }\left(\begin{array}{c}10\\9\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{10}{1024} [/tex]
[tex]\text {Probability of getting 10 correct = }\left(\begin{array}
{c}10\\10\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{1}{1024} [/tex]
P(≥ 4 questions correct):
[tex]\dfrac{210}{1024} + \dfrac{252}{1024} + \dfrac{210}{1024} + \dfrac{120}{1024} + \dfrac{45}{1024} + \dfrac{10}{1024} + \dfrac{1}{1024} = \dfrac{848}{1024} = 0.828[/tex] (3 d.p.)
Answer:P(≥ 40%) = 0.828
Probability of getting correct = 0.5 (because it is a true - false answer)
40% of 10 question = 4 questions
Find P( ≥ 4 questions correct ):
[tex] \text {Probability of getting 4 correct = }\left(\begin{array}{c}10\\4\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{210}{1024} [/tex]
[tex] \text {Probability of getting 5 correct = }\left(\begin{array}{c}10\\5\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{252}{1024} [/tex]
[tex] \text {Probability of getting 6 correct = }\left(\begin{array}{c}10\\6\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{210}{1024} [/tex]
[tex]\text {Probability of getting 7 correct = }\left(\begin{array}{c}10\\7\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{120}{1024} [/tex]
[tex]\text {Probability of getting 8 correct = }\left(\begin{array}{c}10\\8\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{45}{1024} [/tex]
[tex]\text {Probability of getting 9 correct = }\left(\begin{array}{c}10\\9\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{10}{1024} [/tex]
[tex]\text {Probability of getting 10 correct = }\left(\begin{array}
{c}10\\10\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^{10} = \dfrac{1}{1024} [/tex]
P(≥ 4 questions correct):
[tex]\dfrac{210}{1024} + \dfrac{252}{1024} + \dfrac{210}{1024} + \dfrac{120}{1024} + \dfrac{45}{1024} + \dfrac{10}{1024} + \dfrac{1}{1024} = \dfrac{848}{1024} = 0.828[/tex] (3 d.p.)
Answer:P(≥ 40%) = 0.828
