What is the probability of a family having five boys born in a ro...

Question

What is the probability of a family having five boys born in a row? (Assume the probability of a male birth is 1/2.)

Accepted Answer

Welcome back. I'm so glad you're here. We are imagining this certain country has only two weather possibilities. It's either sunny or rainy, nice. Different. Alright. We are given that the probability of a rainy day is going to be one half or 10. and we know that these two possibilities add up together equal 100% the equal one If we're talking about decimals or 100% if we're looking at percentages. And so that means that the probability of it being sunny is going to be 1 -1 half which would just be one half. It's the same as being rainy or 0.5 or 50%. So it is a 5050 shot of being sunny or rainy. We want to figure out the probability that it would be sunny on eight successive days, eight days in a row. Alright. First are these independent of each other these events. So if it's sunny on the first day, does that affect whether it's sunny on the next day? It doesn't these are independent of each other. So we recall from previous lessons that when we have independent events and there are a number of events in this case, there's in this case there's eight of them. So that's the probability of the first event A. And the second event B. And the third event C. And the fourth event D. And the fifth event E. And the sixth event F. Do I know my alphabet and the seventh event G. And the eighth event H. Then we take the probability of the first event times, probability of the second event times the probability of the third event times the probability of the fourth event times the probability of the fifth event times the probability of the sixth event I'm going to lose track times. The probability of the seventh event Times The probability of the 8th event. And what are the probabilities for each of those events? Well, probability for it being sunny on the first day one half, Second day still one half, they don't affect each other's the same probability. Third day still one half, fourth day one half, probability of it's sunny on the fifth day one half and on the sixth day one half, seventh day one half and the eighth day one half. Or writing this a little bit more succinctly. We've got one half raised to the eighth power. We can go ahead and calculate that one half to the eighth power is going to give us one over to 56 which matches with answer choice. A well done. We'll catch you on the next one.