Question

1.) Use the definitions given in the text to find both the odds for and the odds against the following event.

-Flipping 4 fair coins and getting 0 heads.

The odds for getting 0 heads are what to what.​(Type a whole​ number.)

The odds against getting 0 heads are what to what. (Type a whole number)

2.) Determine whether the following individual events are overlapping or​ non-overlapping. Then find the probability of the combined event.

Getting a sum of either 4 or 8 on a roll of two dice

Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.

3.)Determine the probability of having 2 girls and 3 boys in a 5​-child family assuming boys and girls are equally likely.  

The probability of having 2 girls and boy sis is?

4.) Use the​ "at least​ once" rule to find the probabilities of the following event.

Getting at least one head when tossing seven fair coins

Answer 1

1) no. of events corresponding to flipping 4 coins= =16

no. of events where heads don't appear=1

no. of events where heads don't appear=15

therefore odds of getting 0 heads =1/15

odds against getting 0 heads=15/1

2)events where the sum is 4={(1,3),(2,2),(3,1)}

events where the sum is 8={(2,6),(3,5),(4,4),(5,3),(6,2)}

the events are not overlapping as no common element is there in both the events

no. of events where sum is 4=3

no. of events where sum is 8=5

total no. events=6*6=36

therefore the probability of getting a sum kof 4 or 9=(3+5)/36=2/9

3)since the boys and girls are equally likely events

probability of each event=1/2

therefore probability of 2 girls and 3 boys is== 10/32=0.3125

here is the no. of ways 2 girls and 3 boys can be arranged in terms of the time they are born and 1/2 the probability of each of the 5 events of a boy or girl being born

4)no. of events of flipping 7 coins and getting no head=1

total no. of events of flipping 7 coins==128

probability of getting no head=1/128

probability of getting atleast one head=1-P(no head) = 1-(1/128) = 127/128