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junior college 2 | H2 Maths
2 Answers Below
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hiii pls helpp with this qn. thankyou!!
Date Posted: 3 weeks ago
Views: 71
P(X = 1)
= P(total score = 4 with no 1s)
= P(2,2)
= 1/6 × 1/6
= 1/36
P(X = 0.5)
= P(total score = 4 with 1s)
= P(1,3) + P(3,1)
= 1/6 × 2/6 + 1/6 × 1/6
= 1/12
P(X = 1.5)
= P(total score = 3)
= P(1,2) + P(2,1)
= 1/6 × 1/6 + 1/6 × 1/6
= 1/18
P(X = -0.5)
= P(1 appears with total not equal to 3 or 4)
= P(1,4) + P(1,5) + P(1,6) +P(4,1) + P(5,1) + P(6,1) + P(1,1)
= 1/6 + (4 + 5 + 6 - 3)/36 + 3/6 × 1/6 + 1/6 × 1/6
= 3/18
P(X = 0)
= 1 - 1/36 - 1/12 - 1/18 - 3/18
= 2/3
x..................-0.5........0........0.5.........1...........1.5
P(X = x)...3/18....2/3.....1/12.....1/36.....1/18
Expected earnings over 20 games
= 20 E(X)
= 20 (1 × 1/36 + 1/2 × 1/12 + 3/2 × 1/18 - 1/2 × 3/18)
= 100/72
= 1.39 (3 s.f)
= P(total score = 4 with no 1s)
= P(2,2)
= 1/6 × 1/6
= 1/36
P(X = 0.5)
= P(total score = 4 with 1s)
= P(1,3) + P(3,1)
= 1/6 × 2/6 + 1/6 × 1/6
= 1/12
P(X = 1.5)
= P(total score = 3)
= P(1,2) + P(2,1)
= 1/6 × 1/6 + 1/6 × 1/6
= 1/18
P(X = -0.5)
= P(1 appears with total not equal to 3 or 4)
= P(1,4) + P(1,5) + P(1,6) +P(4,1) + P(5,1) + P(6,1) + P(1,1)
= 1/6 + (4 + 5 + 6 - 3)/36 + 3/6 × 1/6 + 1/6 × 1/6
= 3/18
P(X = 0)
= 1 - 1/36 - 1/12 - 1/18 - 3/18
= 2/3
x..................-0.5........0........0.5.........1...........1.5
P(X = x)...3/18....2/3.....1/12.....1/36.....1/18
Expected earnings over 20 games
= 20 E(X)
= 20 (1 × 1/36 + 1/2 × 1/12 + 3/2 × 1/18 - 1/2 × 3/18)
= 100/72
= 1.39 (3 s.f)
I missed out on the (1,4) (4,1) (1,5) (5,1) and (1,6), (6,1) cases.
See 2 Answers
Note that, P(X = -0.5) is more complicated than what you presented.
As mentioned in my earlier comment to the OP,
P(X = -0.5)
= P(1 appears with total not equal to 3 or 4)
= P(1,4) + P(1,5) + P(1,6) +P(4,1) + P(5,1) + P(6,1) + P(1,1)
= 1/6 + (4 + 5 + 6 - 3)/36 + 3/6 × 1/6 + 1/6 × 1/6
= 3/18
and consequently,
P(X = 0)
= 1 - 1/36 - 1/12 - 1/18 - 3/18
= 2/3
And hence, there is no mistake in the answer key.
As mentioned in my earlier comment to the OP,
P(X = -0.5)
= P(1 appears with total not equal to 3 or 4)
= P(1,4) + P(1,5) + P(1,6) +P(4,1) + P(5,1) + P(6,1) + P(1,1)
= 1/6 + (4 + 5 + 6 - 3)/36 + 3/6 × 1/6 + 1/6 × 1/6
= 3/18
and consequently,
P(X = 0)
= 1 - 1/36 - 1/12 - 1/18 - 3/18
= 2/3
And hence, there is no mistake in the answer key.
okie ty
ty
done
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clear
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Should be 2,78 after 20 throws
Date Posted:
3 weeks ago
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