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The selection of r objects out of n is done in
many ways.
The total number of selections 10 that we can make from 6+7=13 students is
thus, the sample space of the experiment is 286
A.
<span>"The probability that a randomly chosen team includes all 6 girls in the class."
total number of group of 10 which include all girls is C(7, 4), because the girls are fixed, and the remaining 4 is to be completed from the 7 boys, which can be done in C(7, 4) many ways.
</span>
<span>
P(all 6 girls chosen)=35/286=0.12
B.
"</span>The probability that a randomly chosen team has 3 girls and 7 boys.<span>"
with the same logic as in A, the number of groups were all 7 boys are in, is
</span>
<span>
so the probability is 20/286=0.07
C.
"</span>The probability that a randomly chosen team has either 4 or 6 boys.<span>"
case 1: the team has 4 boys and 6 girls
this was already calculated in part A, it is </span>0.12.
<span>
case 2, the team has 6 boys and 4 girls.
there C(7, 6)*C(6, 4) ,many ways of doing this, because any selection of the boys which can be done in C(7, 6) ways, can be combined with any selection of the girls.
</span>
<span>
the probability is 105/286=0.367
since case 1 and case 2 are disjoint, that is either one or the other happen, then we add the probabilities:
0.12+0.367=0.487 (approximately = 0.49)
D.
"</span><span>The probability that a randomly chosen team has 5 girls and 5 boys.</span><span>"
selecting 5 boys and 5 girls can be done in
</span>
many ways,
so the probability is 126/286=0.44
The total number of selections 10 that we can make from 6+7=13 students is
thus, the sample space of the experiment is 286
A.
<span>"The probability that a randomly chosen team includes all 6 girls in the class."
total number of group of 10 which include all girls is C(7, 4), because the girls are fixed, and the remaining 4 is to be completed from the 7 boys, which can be done in C(7, 4) many ways.
</span>
<span>
P(all 6 girls chosen)=35/286=0.12
B.
"</span>The probability that a randomly chosen team has 3 girls and 7 boys.<span>"
with the same logic as in A, the number of groups were all 7 boys are in, is
</span>
<span>
so the probability is 20/286=0.07
C.
"</span>The probability that a randomly chosen team has either 4 or 6 boys.<span>"
case 1: the team has 4 boys and 6 girls
this was already calculated in part A, it is </span>0.12.
<span>
case 2, the team has 6 boys and 4 girls.
there C(7, 6)*C(6, 4) ,many ways of doing this, because any selection of the boys which can be done in C(7, 6) ways, can be combined with any selection of the girls.
</span>
<span>
the probability is 105/286=0.367
since case 1 and case 2 are disjoint, that is either one or the other happen, then we add the probabilities:
0.12+0.367=0.487 (approximately = 0.49)
D.
"</span><span>The probability that a randomly chosen team has 5 girls and 5 boys.</span><span>"
selecting 5 boys and 5 girls can be done in
</span>
many ways,
so the probability is 126/286=0.44
The Compound Interest of 10400 at 12.7% for 4 years is 6378.
The principal amount is given as 10400.
The rate of interest is given as 12.7%.
The time period to be calculated is given as 4 years.
The compound interest for the given above is to be calculated.
<h3>What is compound interest?</h3>Compound interest is the interest that we earn both on the principal amount and the interest we earn.
The formula used to calculate compound interest is:
Where P = principal amount, R = rate of interest, and n = number of years.
We have,
P = 10400
R = 12.7%
n = 4 years
Compound interest:
Now,
10400 [ ( 1 + 0.12.7 )^2 - 1 ]
10400 [ 1.127^4 - 1 ]
10400 [ 1.61322 - 1 ]
10400 x 0.6132
6377.56
Rounding to the nearest whole number.
We have,
Compound Interest = 6378.
Thus the Compound Interest of 10400 at 12.7% for 4 years is 6378.
Learn more about Compound Interest here:
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