Question

5. (A: 6 marks and C: 4 marks) (a) Determine the odds against flipping exactly two heads if a coin is tossed three times. (b) Use two examples to explain how odds are different from probability.

Answer 1

(a)

Sample space={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} where H stands for head and T stands for tail.

Odds in against of event A =Probability of A^c/Probability of A= P(A^c)/P(A)

where A=event of exactly two heads={HHT,HTH,THH}

then P(A)=3/8

P(A^c)=1-P(A)=1-3/8=5/8

Odds in against of event A=5/8/3/8=5/3

(b)

The probability of an event is defined as the ratio between total no. of favourable cases of the event and total no. of possible cases . Probabilities always range between 0 and 1. The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

Example:

1. If a race horse runs 100 races and wins 25 times and loses the other 75 times, the probability of winning is 25/100 = 0.25 or 25%, but the odds of the horse winning are 25/75 = 0.333 or 1 win to 3 loses.

2. If coin is tossed three times, the probability of getting exactly two heads=3/8, but the odds of getting exactly two heads=3/8/5/8=3/5 i.e. 3 exactly 2 heads to 5 no head, one head or three heads.