# Probability

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1.John puts the letters of the word FOOTFEST in 8 different envelopes. Paul chooses an envelope at random.
(a)(i)Calculate the probability that Paul chooses an envelope containg letter O (1/8 ?)
(ii)Calculate the probability tthat Paul doesn't chooses an envelope(5/8?) containing the letter E or the letter T

Points are to be won depending on the letter chosen;F=6,O=5,T=4,E=3,S=2
(b)(i)Calculate the probability that Paul obtains at least 4 points.
(ii)Calculate the probability that Paul obtains more than 2 points without choosing the letter O.

After selecting an envelope,Paul throws an unbiased coin:-if the coin shows tails,the points are doubled -if the coin shows heads,the points remain the same.
After selecting an envelope and after throwing the coin,the possible points obtained are:2,3,4,5,6,7,8,10,12
(c)(i)Calculate the probability that Paul obtains 6 points
(ii)Calculate the probability that Paul obtains no more than 10 points.

2.The daily production from a car factory=3 different models-A,B,C which are in two different colours-R and S.
Daily the factory produces 1600 model A cars,800 of model B and 600 of model C. Overall,40% of the cars are of colour R,60% of colour S.60% of of the model A cars are of colour R.
As a percentage of production,there are 3 times as many colour R cars of model B compared to that of model C.
(a)Show that 192 model B cars of colour R are produced daily.
((b)Put the info all this info in a table)
(c)If a car is chosen at random,calculate the probability that it is a model C car in colour S.
(d)Two cars are selected at random from a day's production.Calculate the probability that:
(i)neither of the cars is a model C in colour S.
(ii)at least one car's a model C in colour S.
(iii)the two cars are both model C but of different colours.
(iv)the two cars have the same colour.

• Probability -

1a(i) there are two O's, so P=(2/8)
1b(i) 4+ points are received with F1,F2,O1,O2,T1, and T2, so P=(6/8)
1b(ii) first toss O1 and O2. 3+ points are receive with F1,F2,T1,T2 and E. so P=(5/6)

In 2, put your information into a spreadsheet or table, and take it from there