Rose Harrison and Clara Huizink Solutions for Exercise 14: Practice 5

A group of $30$ children are asked if they play lacrosse$\left(L\right)$, basketball$\left(B\right)$, volleyball$\left(V\right)$ or none of these sports. The results are:

$3$ children do not play any of these sports, $2$ children play all three sports, $6$ play volleyball and basketball, $3$ play lacrosse and basketball,  $6$ play lacrosse and volleyball,
$16$ play basketball, $12$ play volleyball.

Calculate the probability (in the least form a ratio) that a child selected at random:  plays only lacrosse.

A group of $30$ children are asked if they play lacrosse$\left(L\right)$, basketball$\left(B\right)$, volleyball$\left(V\right)$ or none of these sports. The results are:

$3$ children do not play any of these sports, $2$ children play all three sports, $6$ play volleyball and basketball, $3$ play lacrosse and basketball,  $6$ play lacrosse and volleyball,
$16$ play basketball, $12$ play volleyball.

Calculate the probability that a child selected at random:  plays only volleyball.

A group of $90$ students filled in a questionnaire about their free-time activities. The three most popular choices were: go to the cinema $\left(C\right)$, read $\left(R\right)$ and watch television $\left(T\right)$. The results were:

$26$ students watch television, read and go to the cinema
$20$ students watch television and go to the cinema only
$18$ students read and go to the cinema only
$10$ students read and watch television only
$60$ students watch television, $60$ students read, $70$ students go to the cinema.
Draw a Venn diagram to display this information.

A group of $90$ students filled in a questionnaire about their free-time activities. The three most popular choices were: go to the cinema $\left(C\right)$, read $\left(R\right)$ and watch television $\left(T\right)$. The results were:

$26$ students watch television, read and go to the cinema
$20$ students watch television and go to the cinema only
$18$ students read and go to the cinema only
$10$ students read and watch television only
$60$ students watch television, $60$ students read, $70$ students go to the cinema.

Calculate the probability(in the lowest form of a ratio) that a student picked at random: only watches television.

A group of $90$ students filled in a questionnaire about their free-time activities. The three most popular choices were: go to the cinema $\left(C\right)$, read $\left(R\right)$ and watch television $\left(T\right)$. The results were:

$26$ students watch television, read and go to the cinema
$20$ students watch television and go to the cinema only
$18$ students read and go to the cinema only
$10$ students read and watch television only
$60$ students watch television, $60$ students read, $70$ students go to the cinema.

Calculate the probability (in the lowest form of a ratio) that a student picked at random only goes to the cinema.

Of $150$ new university students, $65$ of them study Arabic, $80$ study Chinese and $50$ students study both languages. Calculate the probability (in the least form of a ratio) that a student selected at random studies only Arabic.

Of $150$ new university students, $65$ of them study Arabic, $80$ study Chinese and $50$ students study both languages.

Calculate the probability that a student selected at random studies: only Chinese.

Of $150$ new university students, $65$ of them study Arabic, $80$ study Chinese and $50$ students study both languages.

Calculate the probability that a student selected at random studies: neither Arabic nor Chinese.