Algebra quiz

Probability Level 1

An algebra quiz has three questions. For each question, one (1) mark will be awarded for a correct answer and no mark for a wrong answer. If the probability that Mary correctly answers a question in a quiz is 2 3 \frac{2}{3} , determine the probability that Mary gets 2 2 marks.

1 3 \dfrac{1}{3} 2 3 \dfrac{2}{3} 3 4 \dfrac{3}{4} 4 9 \dfrac{4}{9}

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

The probability of getting a correct answer is 2 3 \dfrac{2}{3} , then the probability of not getting a correct answer is 1 3 \dfrac{1}{3} . The probability that Mary gets two marks in three questions is:

P = n C r p r q n − r = 3 C 2 ( 2 3 ) 2 ( 1 3 ) 1 = 3 ( 4 9 ) ( 1 3 ) = P= _nC_r p^r q^{n-r}=_3C_2\left(\dfrac{2}{3}\right)^2 \left(\dfrac{1}{3}\right)^1=3\left(\dfrac{4}{9}\right)\left(\dfrac{1}{3}\right)= 4 9 \boxed{\dfrac{4}{9}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...