if a fair coin is tossed 4 times, what is the probability of getting heads the first 3 times, and tails the fourth itme?
So you want
HHHT
prob(HHHT) = (1/2)(1/2)(1/2)(1/2) = 1/16
To calculate the probability of getting a specific outcome in a sequence of independent events, you multiply the probabilities of each individual event.
In this case, we have a fair coin being tossed 4 times. Since the coin is fair, the probability of getting heads or tails is both 0.5 (assuming the coin is unbiased).
To find the probability of getting heads the first 3 times and tails the fourth time, we need to multiply the probability of getting heads (0.5) for each of the first three tosses, and then multiply it by the probability of getting tails (0.5) on the fourth toss.
P(Heads, Heads, Heads, Tails) = P(Heads) × P(Heads) × P(Heads) × P(Tails)
= 0.5 × 0.5 × 0.5 × 0.5
= 0.0625 or 6.25%
Therefore, the probability of getting heads the first three times and tails the fourth time when tossing a fair coin 4 times is 6.25%.