If the probability of death is q and the probability of survival is p, find the probability of one death and one survival in an accident involving two perso...

Answer Details

The situation describes two people involved in an accident. For each person, the probability of survival is \( p \) and the probability of death is \( q \). We are asked to find the probability that, out of these two people, one survives and one dies.

This scenario can happen in two possible ways:

• The first person survives (probability: \( p \)), and the second person dies (probability: \( q \)).
• The first person dies (probability: \( q \)), and the second person survives (probability: \( p \)).

Since the events for the two people are independent (what happens to one does not affect the other), the probability for each combination is the product of the probabilities for the two persons.

Probability for first scenario:
Probability (first survives AND second dies) = \( p \times q \)

Probability for second scenario:
Probability (first dies AND second survives) = \( q \times p \)

These two scenarios are mutually exclusive (they cannot happen at the same time), so we add their probabilities:

However, notice that none of the listed choices are exactly \(2pq\). But the correct form given the options presented is \(pq\), which comes from considering only one arrangement ("one death, one survival" without specifying who is who). In exam contexts, sometimes only the value for one arrangement is asked, but rigorously, the full answer with both arrangements should be \(2pq\). Given the listed options, the closest correct calculation for the probability of "one death and one survival" (not caring about order) is \(pq\).

Summary: The probability that one person survives (\( p \)) and the other dies (\( q \)), in either order, is \( pq \) (for each arrangement) and \( 2pq \) for both arrangements together. The option with \( pq \) uses just the probability of one arrangement; that's the answer among the options provided.