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A weather report says that the odds in favour of rain tomorrow are 3 to 5…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A weather report says that the odds in favour of rain tomorrow are $3$ to $5$ . Find the probability of rain and the probability of no rain. On another day, the probability that a train is late is $0.28$ . Write the odds in favour of a late train in the form $a : b$ in lowest terms, and give $a$ and $b$ .

Need a reminder? The key ideaShow

For equally likely outcomes, $P(E) = \dfrac{n(E)}{n(S)}$ . In general the probabilities of the simple events are at least $0$ and add up to $1$ , and $P(E') = 1 - P(E)$ . For at least one, use $1 - P(\text{none})$ . Odds of $a : b$ in favour mean $P = \dfrac{a}{a + b}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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