Question

Consider tossing a coin and rolling a four-sided die (with the numbers 1 through 4 printed on the sides).

(a) Describe the sample space.

(b) Whatistheprobabilityofrollingaheadsandanevennumber?

(c) What are the odds of rolling a heads and an even number?

(d) Whatistheprobabilityofrollingaheads?

(e) What are the odds against rolling a heads?

Determine whether or not the following statements are correct or incorrect and explain why (Be thorough and clear in your explanation!):

(a) A person says “the odds of rolling a 1 on a standard six-sided die is 1/6.”

(b) Inthepastfiveseasons,crosstownfootballrivalstheQuakersandtheCometshaveplayed

each other with the Comets winning twice and the Quakers winning three times. Someone

says “the odds in favor of the Quakers winning are 3:5.”

(c) If the odds in favor of an event occurring are A to B, then the probability of the event

occurring is A/(A+B).

(d) Aneventwithprobability75%meansthattheeventisthreetimesmorelikelytooccurthan

not occur.

Answer 1

(a) The sample space of tossing a coin and rolling afour sided die is

(b) Now, the total number of outcomes =8

So, the probability of rolling a heads and an even number =  

(c) The odds for an event is the ratio of the number of ways the event can occur to the number of ways it does not occur.

Then, the odds of rolling a head and an even number= 2 : 6 = 1 : 3

(d)  Now, the probability of rolling a head =

(e) Hence the odds of rolling a heads are 1 : 1.

(A) a person says "the odds of rolling a 1 on a standard six sided die is 1/6".

This statement is incorrect because the probability of rolling a 1 on a six sided die is 1/6, while the odds are 1:5.

The odds of event = # event occurs : # event does not occur.

(B) This statement is incorrect. The probability of Quakers winning is 3/5. While the odds in favour of Quakers winning are 3 : 2. Always remmember the sum of the odds of an event is equals to the total number of events.

(C)  This is correct. If the odds in favour of an event are A : B, then the total number of events is A+B and The nuber of favourable events is A.

Hence, the probability of event occuring is A/(A+B).

(D) This is correct. let us see it this way

Probability = 75% = 75/100 = 3 / 4

Hence, the odds in favour of the event are 3 : 1.

As the odds of event = # event occurs : # event does not occur.

Therefore, the event is three times more likely to occur than not.