Data on the $30$ largest bond funds provided one$-$year and five year percentage returns for the

period ending March, $312023.$ Suppose we consider a one$-$year return in excess of $2\%$ to be high

and a five$-$year return in excess of $44\%$ to be high. One$-$half of the funds had a one$-$year return

in excess of $2\%,12$ of the funds had a five$-$year return in excess of $44\%,$ and six of the funds had

both a one$-$year return in excess of $2\%$ and a five$-$year return in excess of $44\%..$ If one fund is

selected at random, find the following:

$4\mathrm{.}1.$ The probability that the fund has a high one$-$year return;

$4\mathrm{.}2.$ The probability that the fund has a high five$-$ year return;

$4\mathrm{.}3.$ The probability that the fund has a high one$-$year return and a high five$-$year return;

$4\mathrm{.}4.$ The probability that the fund has a high one$-$year return or a high five$-$year return.

$4\mathrm{.}5.$ The probability that the fund has a high one$-$year return given that the fund has a high five$-$

year return.