Question

Consider a fair coin, such that the probability of observing a head or a tail in a random toss is 0.5. Consider an experiment in which the coin is tossed twice and the two outcomes (O1 and O2) are recorded. Obviously, the probability of observing one head and one tails is 0.5 and the probability of observing both heads or both tails is 0.25 each. Consider the following two probabilities: Given the knowledge that there is at least 1 tails, the probability that there is one head observed is pa. If O1 is heads, the probability that O2 is tails is pb Which of the following statements are true: a) pa is 1/2 and pb is 1/2 b) pa is 1/3 and pb is 2/3 c) pa and pb are not equal d) pa is 2/3 and pb is 1/3

Answer 1

Applying probability concepts, it is found that the correct statements are:

• c) pa and pb are not equal
• d) pa is 2/3 and pb is 1/3

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• A probability is the number of desired outcomes divided by the number of total outcomes.

The sample space, that is, the possible outcomes for the coin tosses is given next, considering H for heads and T for tails.

H - H

H - T

T - H

T - T

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• Considering that there is at least 1 tails, the new sample space is:

H - T

T - H

T - T

• pa: probability of one head, two outcomes with 1 head out of three, thus, pa = 2/3.
• pb: probability that the second is tails, so one outcome(T - T) out of three, thus pb = 1/3.

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The correct statements are:

• c) pa and pb are not equal
• d) pa is 2/3 and pb is 1/3

A similar problem is given at brainly.com/question/14798120