225 times
The expected number is 3750.
When flipping four fair coins, the number of ways to get exactly three heads can be calculated using combinations. Specifically, there are ( \binom{4}{3} = 4 ) ways to choose which three coins will land on heads. The probability of any specific combination of three heads and one tail is ( \left(\frac{1}{2}\right)^4 = \frac{1}{16} ). Therefore, the total probability of getting exactly three heads is ( 4 \times \frac{1}{16} = \frac{4}{16} = \frac{1}{4} ) or 25%.
With 5 coin tosses there are 32 possible outcomes. 10 of these have exactly 2 heads, and 26 of these have 2 or more heads.For exactly two coins are heads: 10/32 = 31.25%For two or more heads: 26/32 = 81.25%
Half the time they will be the same, half the time they will be different. Half of the time that they're the same they will be heads, half the time they are the same they will be tails. It's your homework, YOU figure it out. The way I figure it. There are four options: 1) heads / heads 2) heads / tails 3) tails / heads 4) tails / tails By process of chance, one out of four times both coins will be heads/heads. Therefore 780/4 = 195 times.
When flipping two coins, the probability of both landing on heads in a single flip is ( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} ) or 25%. If you flip the coins 20 times, the expected number of times both will land on heads is ( 20 \times \frac{1}{4} = 5 ). Thus, while the odds for any single flip remain at 25%, over 20 flips, you would expect about 5 occurrences of both coins landing on heads.
around 45
75% is not correct. The odds of flipping 4 independent coins is the same as flipping one coin 4 times. The number of outcomes of 4 flips is 2^4 or 16. The number of ways to exactly get 3 Heads is 4 (THHH, HTHH, HHTH, HHHT) so your chance of flipping 3 heas is 4/16 or 25%. If you include the occurance that produced 4 of 4 Heads, then you get 5/16 or 31.25%.
The odds of getting 3 heads in a toss of 3 coins is 1 in 8, or 0.125. Each coin is probabalistically unrelated to each other, so you simply multiply the odds for each coin. 1 in 2 times 1 in 2 times 1 in 2 is 1 in 8.
To find the probability of getting exactly two heads when tossing a coin three times, we first determine the total number of possible outcomes, which is (2^3 = 8). The favorable outcomes for getting exactly two heads are: HHT, HTH, and THH, totaling 3 outcomes. Therefore, the probability of getting exactly two heads is ( \frac{3}{8} ).
This is a binomial probability distribution The probability of exactly 2 heads in 50 coin tosses of a fair coin is 1.08801856E-12. If you want to solve this for how many times 50 coin tosses it would take to equal 1 time for it to occur, take the reciprocal, which yields you would have to make 9.191019648E11 tosses of 50 times to get exactly 2 heads (this number is 919,101,964,800 or 919 billion times). If you assume 5 min for 50 tosses and 24 hr/day tossing the coin, it would take 8,743,360 years. That is the statistical analysis. As an engineer, looking at the above analysis, I would say it is almost impossible flipping the coin 50 times to get exactly 2 heads or I would not expect 2 heads on 50 coin tosses. So, to answer your question specifically, I would say none.
This is a binomial probability distribution The probability of exactly 2 heads in 50 coin tosses of a fair coin is 1.08801856E-12. If you want to solve this for how many times 50 coin tosses it would take to equal 1 time for it to occur, take the reciprocal, which yields you would have to make 9.191019648E11 tosses of 50 times to get exactly 2 heads (this number is 919,101,964,800 or 919 billion times). If you assume 5 min for 50 tosses and 24 hr/day tossing the coin, it would take 8,743,360 years. That is the statistical analysis. As an engineer, looking at the above analysis, I would say it is almost impossible flipping the coin 50 times to get exactly 2 heads or I would not expect 2 heads on 50 coin tosses. So, to answer your question specifically, I would say none.
Since the probability is 1/4, the number of times this will happen will likely be close to 68 divided by 4.