Question 23. To determine
What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up heads?
The conditional probability is
A coin is flipped five times and the first flip is heads.
Formula used are:
Exactly heads will appear out of the flips if and only if the remaining flips all come up heads. The probability of this is
One can also compute the answer by labelling the event that the first coin flip comes up tails.
Then the probability that a total of heads will appear given that the first flip came up tails is
The conditional probability is .
Question: An electronics company is planning to introduce a new camera phone. The company commissions a marketing report for each new product that predicts either the success or the failure of the product. Of new products introduced by the company, 60% have been successes. Furthermore. 70% of their successful products were predicted to be successes, while 40% of failed products were predicted to be successes. Find the probability that this new camera phone will be successful if its success has been predicted.
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