Final answer:
The probability that it will rain tomorrow is 48.4%, calculated by multiplying the probability that it will be cloudy (55%) by the probability that it will rain if it is cloudy (88%).
Step-by-step explanation:
To find the probability that it will rain tomorrow, we need to consider both the chance of it being cloudy and the chance of it raining if it is cloudy. First, calculate the probability of both events occurring together by multiplying the probabilities of each event. The probability it will be cloudy is 55%, or 0.55. If it is cloudy, the chance that it will rain is 88%, or 0.88. To find the joint probability of it being cloudy and raining, multiply 0.55 (the probability of it being cloudy) by 0.88 (the probability of rain given it's cloudy).
Joint probability of cloudy and raining = 0.55 * 0.88
Joint probability of cloudy and raining = 0.484, or 48.4%
There's a 48.4% chance that it will be cloudy and that it will rain tomorrow. This means the overall probability of rain is 48.4% assuming that it can only rain if it's cloudy.