Question

Calculate the following questions: (i) Calculate the probability of: 2 (a) Tossing four coins and all coming out Heads; 2 (b) The first two numbers coming out in the UK Lottery being in the 30s; 2 (c) Being the fourth person selected from a group of 12; 2 (d) Taking a brown chip from each of three bags, all with 16 chips in total of which 8 are brown in one bag, 10 are brown in another bag and 6 are brown in the final bag; (ii) In a factory, there were 18 accidents involving machinery in the last six months. 2 (a) State the probability distribution that can describe the number of accidents in the factory in any single month; 2 (b) Calculate the probability that there will be 2 accidents in the factory next month; 3 (c) Calculate the probability that there will be less than 3 accidents in the factory during the next two months.

Answer 1

2) a) - 2 - 11 I 2 = 2 16 So there are group. If you Probability of head in a coin The torring outcome of 4 coins is independent of each other P (Head on all 4 wins) = P(Head on 1st win) xP (head on and win) XP (Head on 3rd coin) x P(head on 4th coin) L b) In UK lottery 6 numbers are selected from 1-59. Getting numbers in the 30 means (30-39). 10 numbers to be selected from 59 number for the list no in in 30's) = For the 2nd spot there are 58 number left and 9 of them are in 30's from 30's have already been picked PC and no. is in 30's) p(first 2 no from 301) 45 1711 There are 12 people in the I have been picked in 4th I we can assume that I was not available for spot. spot ¿ P(first olen 1. number 9 58 10x9 = 59x 58 2) A put then st koff 3

.. P (being fu pick out of 12) =P (not 1st pick out of 12) 1st pick out of 12) * P(not and pick out off) P(not 3rd pick out of 10) x P(4th pick out of a) = Х 12 이고 io 11 to 10 = -la i2 = ol 16 2d) P(Picking brown chips from tot bag) P( Picking brown chip from 2nd bag Ja lo P(picking brown Chip from 3rd beg) 16 ܢܘܢ 6 16 . P(taking brown chip from each bag) 8 T6 16 6 16 15 128