A penny, nickel, dime, and a quarter are tossed. What is the probability of the event of obtaining at least three heads on the tosses?
To calculate the probability of obtaining at least three heads on the tosses, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Possible Outcomes:
Since we are tossing 4 coins (penny, nickel, dime, and quarter), each coin has 2 possible outcomes (heads or tails). Therefore, the total number of possible outcomes is 2 * 2 * 2 * 2 = 16.
Number of Favorable Outcomes:
To obtain at least three heads, we have the following possibilities:
1. HHHH - All four coins showing heads.
2. HHHT, HHTH, HTHH, THHH - Three coins showing heads and one showing tails.
3. HTTH, TTHH, THTH, HHTT, HTHT, THTT, TTTH - Two coins showing heads and two showing tails.
4. TTTT - All four coins showing tails.
Counting these possibilities, we have a total of 1 + 4 + 6 + 1 = 12 favorable outcomes.
Probability:
The probability of an event is defined as the number of favorable outcomes divided by the number of total outcomes.
Therefore, the probability of obtaining at least three heads on the tosses is 12/16 = 3/4, which can also be expressed as 0.75 or 75%.
So, the probability of the event is 3/4 or 75%.