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If a heterozygous male with the genotype Ww is mated with a homozygous recessive female of genotype ww, there is a chance that [tex]$\square$[/tex] of the offspring will be heterozygous.

[tex]\[
\begin{array}{|c|c|c|}
\hline
& w & w \\
\hline
w & Ww & ww \\
\hline
w & Ww & ww \\
\hline
\end{array}
\][/tex]

If the heterozygous, Ww, is crossed with a homozygous dominant, WW, then the probability of having a homozygous recessive offspring is:

[tex]\[
\begin{array}{|c|c|c|}
\hline
& W & w \\
\hline
W & WW & Ww \\
\hline
W & WW & Ww \\
\hline
\end{array}
\][/tex]

Let's solve the genetics problem step-by-step!

### Scenario 1:
We are considering a cross between a heterozygous male (Ww) and a homozygous recessive female (ww).

Possible Genotypes of Offspring:
- The male parent contributes either W or w.
- The female parent can only contribute w.

Let's list out the combinations:
- From (Ww) x (ww), the possible offspring are:
- Ww (W from male and w from female)
- ww (w from male and w from female)
- Ww (W from male and w from female)
- ww (w from male and w from female)

Probability Calculation:
- There are two heterozygous (Ww) combinations.
- Out of four total combinations (Ww, ww, Ww, ww), the chance of having heterozygous offspring (Ww) is 2 out of 4.

So, the probability that the offspring will be heterozygous is [tex]$ \frac{2}{4} = 0.5 $[/tex] or 50%.

### Scenario 2:
Now, we'll look at a cross between a heterozygous individual (Ww) and a homozygous dominant individual (WW).

Possible Genotypes of Offspring:
- The heterozygous parent (Ww) can contribute W or w.
- The homozygous dominant parent (WW) can only contribute W.

Possible combinations are:
- WW (W from both parents)
- Ww (W from either parent and w from the heterozygous parent)

- WW (W from both parents)
- Ww (W from either parent and w from the heterozygous parent)

Probability Calculation:
- There are no combinations where both contribute 'w' to produce 'ww', which would be homozygous recessive.

So, the probability of having homozygous recessive (ww) offspring in this cross is 0%.

In summary:
- 50% chance of having heterozygous (Ww) offspring in the first scenario.
- 0% chance of having homozygous recessive (ww) offspring in the second scenario.