A scientific study indicates that if there is an explosive volcanic eruption (Event A) in the tropics, the probability of an El Nino event (Event B) during the following winter increases significantly. (An El Nino event is the periodic warming of sea surface temperatures in the Pacific Ocean near the equator that can cause weather changes in many parts of the world.) Historically, the chances of an El Nino event are about 1 in 4, but the study indicates that that probability increases to about 1 chance in 2 after an explosive eruption. If there is a 60% probability of an explosive volcanic eruption in the tropics this year
a. how likely is it that both events—an eruption and an El Nino event—will happen (assuming the study is correct)?
b. how likely is it that both events will happen if the study is wrong and the events are, in fact, statistically independent (i.e., tropical volcanic eruptions don’t affect the likelihood of an El Nino event)?