A coin is tossed three times. Find the probability of each event.
a) at least two tosses come up tails.
b) at least one toss comes up heads.
PLEASE SHOW ALL WORK!
PLEASE SHOW ALL WORK!
To find the probability of each event, we need to consider the possible outcomes and the total number of outcomes.
Let's start by listing all possible outcomes when a coin is tossed three times.
Possible outcomes:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
a) Event: At least two tosses come up tails.
Possible outcomes with at least two tails: TTH, THT, HTT, TTT (4 outcomes)
Total number of outcomes: 2^3 = 8
Therefore, the probability of at least two tosses coming up tails is 4/8 or 1/2.
b) Event: At least one toss comes up heads.
Possible outcomes with at least one head: HHH, HHT, HTH, THH (4 outcomes)
Total number of outcomes: 2^3 = 8
Therefore, the probability of at least one toss coming up heads is 4/8 or 1/2.
So, the probabilities are:
a) 1/2
b) 1/2