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tmua.me Tau Paper 2 · Q17

Paper 2ProbabilityLogic & proof

Ten coins are tossed together. For every choice of three of the coins, each of the eight possible patterns of heads and tails for those three coins has probability 18\frac18. No other independence is assumed.

Let XX be the number of heads. It is also given that

Pr⁡(X≥8)=320.\Pr(X\ge8)=\frac3{20}.

What is the set of all possible values of Pr⁡(X≤2)\Pr(X\le2)?

A[145,7100]\left[\dfrac1{45},\dfrac7{100}\right]
B(140,7100)\left(\dfrac1{40},\dfrac7{100}\right)
C[132,536]\left[\dfrac1{32},\dfrac5{36}\right]
D[140,18]\left[\dfrac1{40},\dfrac18\right]
E[140,7100]\left[\dfrac1{40},\dfrac7{100}\right]

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