Q. 104.7( 30 Votes )

# Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?

Answer :

Given: : let E_{1} be the event that the outcome on the die is 5 or 6, E_{2} be the event that the outcome on the die is 1, 2, 3 or 4 and A be the event getting exactly head.

Then

And

As in throwing a coin three times we get 8 possibilities.

{HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

⇒ P(A|E_{1}) = P (obtaining exactly one head by tossing the coin three times if she get 5 or 6)

And P(A|E_{2}) = P (obtaining exactly one head by tossing the coin three times if she get 1,2 ,3 or 4)

Now the probability that the girl threw 1, 2, 3 or 4 with a die, being given that she obtained exactly one head, is P(E_{2}|A).

By using bayes’ theorem, we have:

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PREVIOUSTwo groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.NEXTA manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

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