# 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 ≠ (0.58) (0.52)

Coin tosses are dependent