Question

Explain what is wrong with the following statements. Use complete sentences.

a. If there is a $60\%$chance of rain on Saturday and a $70\%$chance of rain on Sunday, then there is a $130\%$chance of rain over the weekend.

b. The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit.

Short answer

a. Probability is more than $100\%.$To get the probability of independent event they have added their probabilities instead of multiplying with each other.

b. Hit a home is a considered as a successful hit that means a batter hits at least no. of success hit as equal to hit a home run. So, getting a home run can't be more than getting a successful hit.

Step-by-step solution

Given information

a. If there is a $60\%$chance of rain on Saturday and a $70\%$chance of rain on Sunday, then there is a $130\%$chance of rain over the weekend.

b. The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit

Calculation

a. In this question it has mentioned that the probability of getting rain on this weekend is $130\%$which cannot be possible because probability lies from$0to1or0\%to100\%$ it can't be more than $100\%.$Since rain on Saturday is independent of rain on Sunday because it is not necessarily true that if there is a rain on Saturday then it will be on Sunday as well or vice versa.

Here probability has added even when the events are independent. We should multiply the probability of both to get the answer instead to adding.

b. Hits a home run implies that a baseball player hits the ball in such a way that he run around the bases and get back to the strike before the ball reaches back. Ultimately hits a home run is a successful hit. And a successful hit means after hitting the batter came back to the base successfully.

By above mentioned we can easily get to know that hits a home run can never be more than getting a successful hit. So, above statement is false.

Final answer

a. Probability is more than $100\%.$To get the probability of independent event they have added their probabilities instead of multiplying with each other.

b. Hit a home is a considered as a successful hit that means a batter hits at least no. of success hit as equal to hit a home run. So, getting a home run can't be more than getting a successful hit.