You have two biased coins. Coin A comes up heads with probability 1/4. Coin B comes up heads with probability 3/4. However, you are not sure which is which, so you choose a coin randomly and you flip it. If the flip is heads, you guess that the flipped coin is B; otherwise, you guess that the flipped coin is A. What is the probability P[C] that your guess is correct

3/4

Step-by-step explanation:

Probability is the likelihood of an event.

No. of favourable outcomes / Total no. of outcomes

Probability of coin selection : [Both coins have equal likelihood of being chosen]

Prob (Coin A Selection) = 1/2 Prob (Coin B selection) = 1/2

Probability of head & tail by both coins:

Prob (Head / Coin A) = 1/4 Prob (Tail / Coin A) = 1 - [ P (Head/Coin A) ] = 1 - 1/4 = 3/4 Prob (Head / Coin B) = 3/4 Prob (Tail / Coin B) = 1 - [ P (Head/Coin B) ] = 1 - 3/4 = 1/4

Probability of getting head by Coin A : Prob (Coin A) & Prob (Head/CoinA) = 1/2 x 1/4 = 1/8

Probability of getting tail by Coin A : Prob (Coin A) & Prob (Tail/CoinA) = 1/2 x 3/4 = 3/8

Probability of getting head by Coin B : Prob (Coin B) & Prob (Head/CoinB) = 1/2 x 3/4 = 3/8

Probability of getting tail by Coin B : Prob (Coin B) & Prob (Head/CoinB) = 1/2 x 1/4 = 1/8

Probability 'The guess [head from coin B, tail from coin A]:

Prob (Coin A) & Prob (Tail/CoinA) or Prob (Coin B) & Prob (Head/CoinB)

= 3/8 + 3/8 = 3/4