Page 52 - Math SL HB Sem 3

\. Exa mple

A bag contains 6 red balls and 2 green balls. One ball is chosen at random each time.
After noling its colour, the ball is then put back into the bag.
a) Martin did 10 such selections. Calculate the probability that a green ball is selected
i) exactly twice.
ii) more than two times.
b) The selection and replacement process is conducted 70 times by a robot.
What is the expected number of green balls that would be selected?

\. Example:

Factory A makes microphones. The probability that a microphone is faulty is 3 %
A random sample of 50 microphones is tested.
a) Write down the mean number of faulty microphones in the sample.
b) Calculate the probability that no more than 3 microphones are faulty.

) Calculate the probability using the binomial distribution function

Example:

ln a card game, player A randomly draws two cards from a stack of which 5 are black and 2
are white, without replacement.
a) What is the probability that one black and one white card are drawn?

b)After two cards are drawn, the cards are then replaced. lf the player made 20 attempts of
drawing two cards, what is probability that 5 attempts got one black and one white card?

c) Calculate the mean number of draws that one black and one white card are selected out
of the 20 draws.

lz