A man tosses a coin and throws a die beginning with the coin. What is the probability that he will get heads first followed by 5 or 6 on the die.
A coin is tossed first after which a die is rolled. The probability of the coin landing heads up and the die showing 5 or 6 has to be determined.
The probability of getting heads when a coin is tossed is (1/2). The probability of getting 5 when the die is rolled is (1/6) and the probability of getting a 6 when the die is rolled is also (1/6).
If the probability of two events is P1 and P2 and both of them need to occur, the probability of that happening is P1*P2 whereas the probability of either of the two events occurring is P1 + P2.
Here, the probability of getting heads followed by either 5 or 6 is `(1/2)*(1/6 + 1/6) = (1/2)*(2/6) = 1/6`
There is probability of 1/6 that the coin lands head up and the die shows either 5 or 6.