It is (1/2)9 = 1/512
The number of trials: n = 9, the number of success: r = 4. The probability of success: P(H) = 1/2, the probability of failure: P(T) = 1/2. P(exactly 4 heads in 9 tosses) = 9C4 x (1/2)^5 x (1/2)^4 = 126(1/2)^9 = 0.246 P(at most 2 heads) = P(none heads) + P( 1 head) + P(2 heads) = 9C0[(1/2)^9][(1/2)^0] + 9C1[(1/2)^8][(1/2)^1] + 9C2[(1/2)^7][(1/2)^2] = 1(1/2)^9 + 9(1/2)^9 + 36(1/2)^9 = (1 + 9 + 36)(1/2)^9 = 46(1/2)^9 = 0.09
well, it will have 6 times of the greater chance.
2/9
No heads means that every toss lands tails. (0.5)30= 9.3 x 10-10 Note that 109 = 1 trillion, so the probability can be stated this event is likely to occur about 9 times in 10 trillion tosses.
50%.
It is (1/2)9 = 1/512
If you continue tossing the coin forever, it is effectively a certainty. So probability = 1 If you toss it only 9 times, it is (1/2)9 = 1/512 = 0.00195 (approx)
the probability of getting heads-heads-heads if you toss a coin three times is 1 out of 9.
It is 9/36 = 1/4
The number of trials: n = 9, the number of success: r = 4. The probability of success: P(H) = 1/2, the probability of failure: P(T) = 1/2. P(exactly 4 heads in 9 tosses) = 9C4 x (1/2)^5 x (1/2)^4 = 126(1/2)^9 = 0.246 P(at most 2 heads) = P(none heads) + P( 1 head) + P(2 heads) = 9C0[(1/2)^9][(1/2)^0] + 9C1[(1/2)^8][(1/2)^1] + 9C2[(1/2)^7][(1/2)^2] = 1(1/2)^9 + 9(1/2)^9 + 36(1/2)^9 = (1 + 9 + 36)(1/2)^9 = 46(1/2)^9 = 0.09
Prob(Exactly 9 Heads) = 0.0269 Prob(At least 2 Heads) = 0.0327 Prob(At most 8 Heads) = 0.9673
In this case, you should first calculate the probability of NOT rolling either a 3 or a 6. For one die, this probability is 4/6 = 2/3. For two dice, this probability is 2/3 x 2/3 = 4/9. Therefore, the probability that you DO get a 3 or a 6 is 1 - 4/9 = 5/9.
The probability of tossing a coin 9 times and getting at least one tail is: P(9 times, at least 1 tail) = 1 - P(9 heads) = 1 - (0.50)9 = 0.9980... ≈ 99.8%
well, it will have 6 times of the greater chance.
(4!*5!)/9! = .0079
The probability of getting 8 heads out of 10 tosses is (10C8)(1/2)^8 (1/2)^2 = 45 / 1024 = 0.0439. It is assumed that the probability of getting a head in a single toss is 1/2. 10C8 = 10 x 9 / 1 x 2 = 45