Question 24
The probability of rain on a particular day is $3/5$. Andrew and Bella are going home from school. Andrew brings an umbrella with probability $1/3$, and Bella with probability $b$. If it does not rain, the probability that they go home together is $c$. If it rains, they go home together if and only if exactly one of them brings an umbrella. Their overall probability of going home together is $2/5$. If the minimum of $b^2+c^2$ is $\delta$, find $\lfloor100\delta\rfloor$.
Conditional self-study model: assume the two umbrella choices are independent of each other, and that the pair of umbrella choices is independent of whether it rains. The source does not state these assumptions. All probabilities b,c lie between 0 and 1.
Conditional self-study model: assume the two umbrella choices are independent of each other, and that the pair of umbrella choices is independent of whether it rains. The source does not state these assumptions. All probabilities b,c lie between 0 and 1.