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GATE 2015 EE - SET 2 - Question 27

Solution :

P(H_{R}H_{s}) = P(H_{R})P(H_{s})  ---- Coins are independent.

P(H_{R}H_{s}) = 0.28

P(T_{R}T_{s}) = 0.18

P(H_{R}T_{s}) = 0.3

P(T_{R}H_{s}) = 0.24

By total Probability theorem

P(H_{R}H_{s}) +†P(H_{R}T_{s}) = P(H_{R})

0.28 + 0.3 = P(H_{R})

P(H_{R}) = 0.58

P(H_{R}H_{s}) + P(T_{R}H_{s}) = P(H_{s})

0.28 + 0.24 = P(H_{s})

P(H_{s}) = 0.52

P(H_{R}H_{s}) =  P(H_{R})P(H_{s})

0.28¬†‚Ȇ (0.58) (0.52)

Coin tosses are dependent

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