a coin is tossed 5 times what are the odds against the coin showing heads all 5 times
To find the odds against the coin showing heads all 5 times, we need to determine the probability of getting heads in a single toss and then calculate the odds.
The probability of getting heads in a single toss is 1/2 (assuming a fair coin).
The probability of getting heads in all 5 tosses can be calculated by raising the probability of getting heads in a single toss to the power of the number of tosses: (1/2)^5 = 1/32.
Now, let's calculate the odds against this outcome. Odds are determined by dividing the probability of the event not happening by the probability of the event happening.
The probability of the coin NOT showing heads all 5 times is 1 - 1/32 = 31/32.
Therefore, the odds against the coin showing heads all 5 times are 31 to 1.
To calculate the odds against an event, we need to first determine the probability of the event occurring.
In this case, the probability of getting heads on a fair coin toss is 1/2 or 0.5.
To find the probability of getting heads on all 5 tosses, we multiply the individual probabilities:
0.5 × 0.5 × 0.5 × 0.5 × 0.5 = 0.03125
So, the probability of getting heads on all 5 tosses is 0.03125.
Now, to find the odds against this event, we use the formula:
Odds against = (1 - Probability) : Probability
Odds against = (1 - 0.03125) : 0.03125
Odds against = 0.96875 : 0.03125
Simplifying the ratio, we get:
Odds against = 31 : 1
Therefore, the odds against the coin showing heads all 5 times are 31 to 1.