Suppose that we have a box that contains two coins: A fair coin: P (H) = P (T) = 0.5. A two-headed coin: P (H) = 1. A coin is chosen at random from the box, i. e. either coin is chosen with probability 1/2, and tossed twice. Conditioned on the identity of the coin, the two tosses are independent. Define the following events: Event A : first coin toss is H. Event B : second coin toss is H. Event C : two coin tosses result in HH. Event D : the fair coin is chosen. For the following statements, decide whether they are true or false. A and B are independent.

Question

Mathematics

Jensen King

30 May, 03:19

Suppose that we have a box that contains two coins: A fair coin: P (H) = P (T) = 0.5. A two-headed coin: P (H) = 1. A coin is chosen at random from the box, i. e. either coin is chosen with probability 1/2, and tossed twice. Conditioned on the identity of the coin, the two tosses are independent. Define the following events: Event A : first coin toss is H. Event B : second coin toss is H. Event C : two coin tosses result in HH. Event D : the fair coin is chosen. For the following statements, decide whether they are true or false. A and B are independent.

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Answers (1)

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Jamir Goodman · Answer 1

2. True

Step-by-step explanation:

2. The two events are mutually exclusive events. This means that the probabilities on coins 1 and coins 2 are independent on each other. In other words, the probability of the first coin does not affect the probability of the second coin outcome.