Correct answer: 8
Explanation:
When a coin is tossed, it has 2 possible outcomes: Heads (H) or Tails (T). For three coins, each coin can independently show either Heads or Tails. Therefore, the total number of outcomes for three coins is: \[ 2 \times 2 \times 2 = 8 \] The possible outcomes are: \[ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \]
Hence, the total number of outcomes is 8.
If A is any event associated with sample space and if E1, E2, E3 are mutually exclusive and exhaustive events. Then which of the following are true?
(A) \(P(A) = P(E_1)P(E_1|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)\)
(B) \(P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)\)
(C) \(P(E_i|A) = \frac{P(A|E_i)P(E_i)}{\sum_{j=1}^{3} P(A|E_j)P(E_j)}, \; i=1,2,3\)
(D) \(P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{j=1}^{3} P(E_i|A)P(E_j)}, \; i=1,2,3\)
Choose the correct answer from the options given below: