19 ECEN 356 ote: Only a calculator and a formula card are allowed for this quis.

Question

19 ECEN 356 ote: Only a calculator and a formula card are allowed for this quis. All Electronic devices must be off during the test. Q1. Find the number of possible combinations that 8 toys can be given to 3 children with the ages 3, 5, and 8 years old, if the youngest child gets 4 toys and the other two child get 2 toys each Q2: Mark and Tom are to play a tennis tournament. Whoever wins three games in a row or a total of four games wll win the tournament. Show number of possible combination of games that each player has to win in order to win the tournament. 2 5 Q3: Threefair coins are tossed and number of tails is recorded. Let A to be the event that at least one tail appears and B to be the event that no tails or all tails appear. a) What is the sample space S for this experiment and the corresponding probability of each? b) What is the probability of event A, P(A), and event 8, P(B)?

Explanation / Answer

Q1) There are 8 toys and youngest child i.e. 3 year old child should get 4 Toys.

So 4 toys out of 8 toys can be selected in 8C4 ways = 8!/(8-4)!4! = 5*6*7*8/1*2*3*4 = 70 ...........1

Now 5 year child should get 2 toys out of remaining 4 toys.

So 2 toys out of 4 toys can be selected in 4C2 ways = 4!/(4-2)!2! = 1*2*3*4/2*2 = 6     ..............2

Now 8 year child should get 2 toys out of remaining 2 toys.

So 2 toys out of24 toys can be selected in 2C2 ways = 2!/(2-2)!2! = 1*2/1*2 = 1    (0! =1)     ..............3

From 1,2&3 Number of possible combinations 70+6+1 = 77

This is the required answer.

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