= Solution
\b[The observed death fraction is]
$$
\boxed{\widehat\pi=\frac{100}{150}=\frac23.}
$$
In the <independent> two-exponential <competing risks model>, $\pi=\lambda/(\lambda+\gamma)$. Thus the observed fraction estimates the share of the combined rate attributable to death. Combining it with an estimate of $s=\lambda+\gamma$ yields $\widehat\lambda=\widehat\pi\widehat s$ and $\widehat\gamma=(1-\widehat\pi)\widehat s$. This uses the event-type information that the death-only time analysis ignored.
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