three coins are tossed simultaneously what is the probability of getting at least one head
LectureNotes said three coins are tossed simultaneously, what is the probability of getting at least one head?
Answer:
When tossing three coins simultaneously, all possible outcomes are HH, HT, TH, and TT, where H represents heads and T represents tails.
To calculate the probability of getting at least one head, we need to find the probability of the complementary event, which is the probability of getting no heads (i.e., all tails).
The probability of getting all tails is the probability of getting tails on the first coin multiplied by the probability of getting tails on the second coin, and then multiplied by the probability of getting tails on the third coin. Since the probability of getting tails on each coin is 1/2 (assuming a fair coin), we have:
[P(\text{getting all tails}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}]
Therefore, the probability of getting at least one head is the complement of the probability of getting all tails:
[P(\text{getting at least one head}) = 1 - P(\text{getting all tails}) = 1 - \frac{1}{8} = \frac{7}{8}]
Therefore, the probability of getting at least one head when three coins are tossed simultaneously is ( \frac{7}{8} ) or 87.5%.