Pr(3 flips at least one H) = 1 - Pr(3 flips, NO heads) = 1 - Pr(3 flips, TTT) = 1 - (1/2)3 = 1 - 1/8 = 7/8
The probability of getting two tails is 1/4. The probability of something happening is the answer to the question, "What fraction of the time will this happen?" It is the number of ways it can happen, out of all the different things that can happen. With two coin flips, these are all the things that can happen H H H T T H T T There is one way in which you can get two tails, out of four possible things that can happen. One out of four, or 1/4.
Two flips can have four possible results:T - TT - HH - TH - HThe question defines 'success' as either H-T or T-H.Two successes out of four possibilities = probability of 2/4 = 1/2 = 50% .
4: h/h, h/t, t/h & t/t
The sample space consists of all the possible outcomes. A flip of a coin has 2 outcomes, H,T. The total number of outcomes for 6 flips are 26 or 64.
In three flips of a fair coin, there are a total of 8 possible outcomes: T, T, T; T, T, H; T, H, T; T, H, H; H, H, H; H, H, T; H, T, H; H, T, T Of the possible outcomes, four of them (half) contain at least two heads, as can be seen by inspection. Note: In flipping a coin, there are two possible outcomes at each flipping event. The number of possible outcomes expands as a function of the number of times the coin is flipped. One flip, two possible outcomes. Two flips, four possible outcomes. Three flips, eight possible outcomes. Four flips, sixteen possible outcomes. It appears that the number of possible outcomes is a power of the number of possible outcomes, which is two. 21 = 2, 22 = 4, 23 = 8, 24 = 16, .... Looks like a pattern developing there. Welcome to this variant of permutations.
Pr(3 flips at least one H) = 1 - Pr(3 flips, NO heads) = 1 - Pr(3 flips, TTT) = 1 - (1/2)3 = 1 - 1/8 = 7/8
a) 1/16b) 1/16c) 1/256 [this answer was given, but it is unclear what part-c is even asking: The pattern occurs before what pattern? There are many variables which are unspecified and would affect the outcome.]
The tree in which the first set of branches are H and T and then, from each of those nodes, there is a pair of branches which are H and T.
The probability of getting two tails is 1/4. The probability of something happening is the answer to the question, "What fraction of the time will this happen?" It is the number of ways it can happen, out of all the different things that can happen. With two coin flips, these are all the things that can happen H H H T T H T T There is one way in which you can get two tails, out of four possible things that can happen. One out of four, or 1/4.
Two flips can have four possible results:T - TT - HH - TH - HThe question defines 'success' as either H-T or T-H.Two successes out of four possibilities = probability of 2/4 = 1/2 = 50% .
p = -log H= concentration of hydrogen in solution (H+) therefore, pH= -log [H+] or [H+] = 10-pH
pH = -log [H+], so if the [H+] is 2.310 M, the pH = -0.3636
4: h/h, h/t, t/h & t/t
The sample space consists of all the possible outcomes. A flip of a coin has 2 outcomes, H,T. The total number of outcomes for 6 flips are 26 or 64.
pH = -log[H+], where [H+] is the hydrogen ion concentration in moles per liter.
The pH of a 1N HCl solution can be calculated using the formula pH = -log[H+], where [H+] is the concentration of H+ ions in the solution. For a 1N solution of HCl, the concentration of H+ ions will be 1M, so the pH will be -log(1) = 0.