Binomial distribution KUS objectives BAT Use the Binomial

Binomial distribution • KUS objectives BAT Use the Binomial theorem to find single probabilities Starter: find The number of ways of getting 8 heads with 10 coins The number of ways of getting 8 or more heads with 10 coins The number of ways of getting 2 or less heads with 10 coins

Review 1 The Binomial Expansion is; r is effectively the ‘position’ in the expansion n is the power which the bracket is raised to

WB 4

WB 5 Now imagine a biased coin with P(Heads) = p If the coin is thrown 10 times we can use the Binomial theorem to find probabilities. What are p and q ?

WB 6 Now imagine the coin is biased so that the probability of tossing heads is 0. 3 What is the probability of getting 3 heads out of 5 tosses? The probability of each of combinations is found by: 3 heads means 2 tails P(heads) = 0. 3 P(tails) = 1 – P(heads) Is this a high probability? Higher / lower than you expected?

Notes Notation for the Binomial model n called the ‘index’ p is the ‘parameter’

WB 7 A fair die is rolled eight times. Find the probability of rolling a) no sixes b) only 3 sixes c) four twos and 4 sixes

WB 8 We can apply this to other problems – so long as we have independence for probability (i. e. the probability remains constant) A drug is known to be effective on 60% of patients. a) What is the probability that 7 out of 10 treatments work? A drug is known to be effective on 60% of patients. a) What is the probability that 3 out of 10 treatments work?

WB 9

WB 10 IF the claim is correct then it is very unlikely that only 3 cats would prefer the company brand in a sample of ten

Practice Ex 1 B Qs 1 to 4

KUS objectives BAT Use the Binomial theorem to find single probabilities self-assess One thing learned is – One thing to improve is –

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