S 2 Chapter 2 Binomial Distribution Lesson 2

S 2 – Chapter 2 – Binomial Distribution Lesson 2: Binomial Distribution

Frost True Stories Back in 2010 I was on holiday in Hawaii and visited the family of a friend. We noticed that at the dinner table that out of the 8 of us, 6 of us were left-handed (including myself). One of them asked, “The chances of that must be very low”. I saw that as a challenge. Consider the 8 people in a line. Suppose 10% of the population is left-handed. Can you now work out the probability of 6 being left-handed now? ?

Test Your Understanding Q ? ? ?

Binomial Distribution ! So that we’re allowed to multiply the probabilities together from each trial We’re counting heads, so throwing a heads is the “success”. FICT

Quickfire Questions Show the calculation required to find the indicated probability given the distribution. ? ? ?

Is it Binomially Distributed? Is a Binomial Distribution appropriate as a model? Some number out of 8 people being left-handed The number of red balls selected when 3 balls are drawn from bag of 15 white and 5 red balls. Number of throws on die until 6 obtained Number of girls in family of 4 children No, not fixed. This is known as a ‘Geometric Distribution’ (which we won’t cover) ? ? ? Usually. But in my story, genetics has an influence on handedness. Technically the probability of having a girl increases if you previously had a girl, and vice versa. But the probability is still close to 0. 5, so Binomial Distribution is appropriate. ? Only if balls drawn with replacement.

Test Your Understanding Q 1 ? ? Q 2 a b ? ? (If you get these quickly, go on to Exercise 1 B)