Practice section 3 of 8

If the letters of SEPTEMBER are arranged at random, find the probability that (i) the 3 Es are together, (ii) the 3 Es are separated, (iii) not all the 3 Es are together.

If the letters of PROBABILITY are arranged at random, find the probability that the two Is are (i) together, (ii) separated.

A bag contains 5 counters,3 green and 2 white. Two counters are picked at random without replacement. Find the probability that (i) one green and one white are drawn, (ii) at least one green is drawn, (iii) at least one white is drawn, given that at least one green is drawn.

At a petrol station,30%of customers buy leaded petrol,60%buy unleaded petrol and the remainder buy diesel. A leaded-petrol customer has a 25%chance of filling the tank; an unleaded-petrol customer has a 20%chance; a diesel customer has a 30%chance.

(i) Draw a probability tree.

(ii) Find the probability that a car leaving does not have a full tank.

(iii) Given that it has a full tank, find the probability that it contains unleaded petrol.

A factory has three machines A,B,C producing large numbers of an item. Their shares of daily production are 50%,30%,20%, respectively.

Their respective defect rates are 2%,3%,4%. The occurrence of a defective item is independent of all other items.

One item is chosen at random from the day’s total output.

(i) Show that its probability of being defective is 0.027.

(ii) Given that it is defective, find the probability that it was produced on A.

A box contains blue and white discs. The probability of blue is 1/3 and white is 2/3. Two discs are drawn with replacement. Find the probability that (i) both discs are white, (ii) the first is blue and the second white, (iii) the first is blue or the second white.