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GATE 2015 EE - SET 2 - Question 27

Solution :

$P(H_{R}H_{s})$ = $P(H_{R})P(H_{s})$ Â ---- 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 =Â $P(H_{R})$

$P(H_{R})$ = 0.58

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

0.28 + 0.24 =Â $P(H_{s})$

$P(H_{s})$ = 0.52

$P(H_{R}H_{s})$ =Â  $P(H_{R})P(H_{s})$

0.28Â â‰  (0.58) (0.52)

Coin tosses are dependent

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