A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.
Probability of head and 3 on a die is:
P( head and 3 ) = p(head )* P(3)
We multiply probabilities because we have 2 independent events.
We know that p(head) = 1/2
Also p(3) = 1/6
Then P( head and 3) = 1/2 * 1/6 = 1/12
There are two independent events: (i) tossing a coin and rolling 6 sided die.
When we toss an unbiased coin we may get a head or a tail up. So getting head or tail are equally likely . So the probability getting a head = 1/2.
When an unbiased 6 sided die is rolled , we may get any one of the number from 1 to 6. So there are 6 equal choices. Getting 3 is one choice out of 6 choices. So the probability of getting 3 = 1/6.
Since the two events - getting a head in a coin in a toss and getting a 3 in a rolling of die - are independent , the happening of both events is the product of the probabilities = (1/2) (16) = 1/18.
Therefore , the probability of getting a head in a toss of the coin and getting a number 3 in a rolling of a die is 1/18.