Question

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1) The percentage of marks obtained by a student in monthly unit test are given (see the attachment) :

1)A first class i.e. at least 60% marks
2)Marks between 70% to 80%
3)A distinction i.e. 75% or above
4)less than 65% marks

Please provide well-explained answers :)​

Answer 1

Step-by-step explanation:

${\large{\bf{\underline{\red{Given :}}}}}$

• Total no. of tests = 5
• Marks obtained = 58, 74, 76, 62, 85

${\large{\bf{\underline{\red{To \: find :}}}}}$

The probability that the student gets :

• A first class i.e. at least 60% marks
• Marks between 70% to 80%
• A distinction i.e. 75% or above
• Less than 65% marks

We know that,

${\bold{: ⟹ \: \: \: \: \:}} {\bold{\underline{\boxed{\rm{Probability \: of \: an \: event \: = \: \frac{Number \: of \: Favorable \: outcomes}{Total \: Numbers \: of \: outcomes}}}}}}$

${\large{\bf{\underline{\red{Solution :}}}}}$

1. Probability of scoring at least 60%

${\bold{\sf{⟼ \: \: \: \: \: No. \: of \: students \: who \: scored \: first \: class \: = \: 4}}}$

${\bold{\sf{⟼ \: \: \: \: \: No. \: of \: test = \: 5}}}$

${\bold{\sf{⟼ \: \: \: \: \: Probability \: of \: scoring \: first \: class :}}}$

$⟼ \: \: \: \: \:{\bold{\underline{\boxed{\mathfrak{\pink{\ \: \frac{4}{5} \: }}}}}}$

2. Probability of getting between 70% to 80%

${\bold{\sf{⟼ \: \: \: \: \: No. \: of \: students \: who \: scored \: between \: 70\% \: to \: 80\% \: = \: 2}}}$

${\bold{\sf{⟼ \: \: \: \: \: No. \: of \: tests \: = \: 5}}}$

${\bold{\sf{⟼ \: \: \: \: \: Probability \: of \: scoring \: 70\% \: to \: 80\% \::}}}$

${\bold{⟼ \: \: \: \: \: }}{\bold{\underline{\boxed{\mathfrak{\pink{ \: \frac{2}{5} \: }}}}}}$

3. Probability of getting distinction

${\bold{\sf{⟼ \: \: \: \: \: No. \: of \: students \: who \: scored \: above \: 70\% \: = \: 2}}}$

${\bold{\sf{⟼ \: \: \: \: \: Total \: no. \: of \: tests \: = \: 5}}}$

${\bold{\sf{⟼ \: \: \: \: \: Probability \: of \: getting \: distinction \: :}}}$

${\bold{⟼ \: \: \: \: \: }}{\bold{\underline{\boxed{\mathfrak{\pink{ \: \frac{2}{5} \: }}}}}}$

4. Probability of getting less than 65%

${\bold{\sf{⟼ \: \: \: \: \: No. \: of \: students \: who \: score \: less \: than \: 65\% \: = \: 1}}}$

${\bold{\sf{⟼ \: \: \: \: \: Total \: no. \: of \: tests \: = \: 5}}}$

${\bold{\sf{⟼ \: \: \: \: \: Probability \: of \: getting \: less \: than \: 65\% \: :}}}$

${\bold{⟼ \: \: \: \: \: }}{\bold{\underline{\boxed{\mathfrak{\pink{ \: \frac{1}{5} \: }}}}}}$

Answer 2

$\huge{ \boxed{ \bold \red{A}}}{ \boxed{ \bold \green{N}}}{ \boxed{ \bold \blue{S}}}{ \boxed{{{ \bold{W}}}}}{ \boxed {\bold \pink{E}}}{ \boxed {\bold \purple{R}}}$