Question

There is a 30% chance of rain and a 70% chance of shine. If it rains, there is a 50% chance that Bob will cancel his picnic, but if the sun is shining, he will definitely have his picnic. What is the percentage chance that Bob will have his picnic?

• A. $65$
• B. $75$
• C. $55$
• D. $85$

Answer 1

The correct option is D $85$

There is a 30% chance of rain and a 70% chance of shine. If it rains, there is a 50% chance that Bob will cancel his picnic, but if the sun is shining, he will definitely have his picnic.

50% chance that Bob will cancel his picnic in case of a rain means that there is 50% chance that Bob will NOT cancel his picnic in case of a rain. So, $P\left(E\right)=0.3\ast 0.5+0.7\ast 1=0.85$ or 85%.