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Mathematics
Mathematics
Problem
A spinner has three unequal probabilities for its sectors A, B, and C given by
P
(
A
)
=
p
P(A)=p
P
(
A
)
=
p
,
P
(
B
)
=
2
p
P(B)=2p
P
(
B
)
=
2
p
, and
P
(
C
)
=
1
−
3
p
P(C)=1-3p
P
(
C
)
=
1
−
3
p
. For which of the following intervals of
p
p
p
are all three probabilities valid? a)
0
<
p
<
1
2
0 < p < \dfrac12
0
<
p
<
2
1
b)
1
3
<
p
<
1
2
\dfrac13 < p < \dfrac12
3
1
<
p
<
2
1
c)
0
≤
p
≤
1
3
0 \le p \le \dfrac13
0
≤
p
≤
3
1
d)
0
<
p
<
1
3
0 < p < \dfrac13
0
<
p
<
3
1
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