Answer:
Part a: The probability of breaking even in 6 tosses is 0.3125.
Part b: The probability that one payer wins all the money after the 10th toss is 0.0264.
Explanation:
Part a
P(success)=1/2=0.5
P(Failure)=1/2=0.5
Now for the break-even at the sixth toss
P(Break Even)=P(3 success out of 6)
P(3 success out of 6)
So the probability of breaking even in 6 tosses is 0.3125.
Part b:
So the probability that one of the player wins all the money after the 10th toss is given as the tenth toss is given as a win so
Wins in 9 tosses is given as 9!/7!=72
The probability that the other person wins
Wins in 8 out of 10 tosses is given as 10!/8!(10-8)!=10!/8!2!=45
So the probability of all the money is won by one of the gambler after the 10th toss is given as
P=number of wins in 9 tosses-Number of wins in 10 tosses/total number of tosses
P=(72-45)/2^16
P=0.0264
So the probability that one payer wins all the money after the 10th toss is 0.0264.
Answer:
9.635%
Explanation:
We shall use a table to compute different values as shown below.
<u>Investment</u> <u>Return</u> <u>Taxable amount</u> <u>Tax Rate</u> <u>After-tax return</u>
Dividend 9.8% 30% (n1) 18% 9.2708% (w1)
Municipal bond 8.8% 0% 18% 8.8%
Corporate bond 11.75% 100% 18% 9.635% (w2)
The after tax return with on the best investment alternative is 9.635% for corporate bonds
<u>Workings</u>:
W1
9.8 *0.3*0.18 = 0.5292%
Return after tax = 9.8% -0.5292% = 9.2708%
w2
18.75*0.18 =2.115%
Return after tax = 11.75% -2.115% = 9.635%
<u>Notes:</u>
n1 : 70% of the dividends are excluded from taxation. Only 30% is to be taxed
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