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The best way to think about this is the following way:
What is the probability of flipping heads once?
1/2
What is the probability of flipping heads twice?
1/4 (1/2 * 1/2)
Using this we can derive the equation to find the probability of flipping heads any number of times. 1/2n
Using this we plug in 25 for n and get
1/225 or as a decimal 2.98023224 x 10-8
or as odds 1:33,554,432
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A coin is tossed twice what is the probability that it will show heads both times?
The probability is 0.25.Look at it this way--if you toss a coin twice, there are four equally-probable outcomes:tails, tailstails, headsheads, tailsheads, headsSo the probability of heads twice in a row is one in four, or 25%.the chance of tossing heads is 1/2 (50%) The chance of tossing the next heads is 1/2 (50%) 1/2 x 1/2 = 1/4 (25%)
What is the probability of getting three heads if you flip four coins?
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%.
If I were to flip a coin 2 times. What is the probability of getting heads?
25%
What is the probability of getting a even number and a head when rolling a die and then tossing a coin?
A die has six sides, so the probability of rolling an even number is 1 in 2, or 50-50. A coin has two sides, so the probability of flipping the coin and getting heads is 1 in 2, or 50-50. The probability that both will happen together is the one in two OF one in two, or one in FOUR chance that both will happen. So, the probability is 25%.
What is the probability of rolling a 4 or 6 and flipping heads twice and picking up a Jack?
These are all independent events (flipping a coin will not affect the probability of drawing a Jack) so you can get the probability of all events occurring by multiplying together the probabilities of each event occurring. In other words: P (4 or 6, 2 heads, Jack) = P(4 or 6) * P(2 Heads) * P(Jack) Now we need to look at each probability separately. Remember that: Probability = Successful Outcomes / (Successful Outcomes + Unsuccessful Outcomes) In the case of rolling a die, a successful outcome (as defined in the problem) is rolling a 4 or 6. An unsuccessful outcome is everything else (1, 2, 3, or 5). Using the formula above then: Probability (4 or 6) = 2/6 = .33 Figuring out the probability of rolling two heads is slightly different because we are talking about two flips not one. In this case we have to go back to our original formula for multiple events. Probability (2 Heads) = Prob(Head) * Prob(Head) Since we know a coin-toss has a 1/2 chance of being heads or tails: Probability (2 Heads) = .5 * .5 = .25 Finally, in the case of picking up a card from a deck, a successful outcome (as defined in the problem) is picking a Jack. There are 4 Jacks in a standard deck so there are 4 possibilities of a successful outcome. There are 48 cards in a stardard deck that are not Jacks. Therefore: Probability (Jack) = 4/52 = .077 Now we can plug these values into our combination formula to get our answer. P (4 or 6, 2 heads, Jack) = P(4 or 6) * P(2 Heads) * P(Jack) P (4 or 6, 2 heads, Jack) = .33 * .25 * .077 = .00635 There is a .635% chance of rolling a 4 or 6, flipping a heads twice, AND drawing a Jack.
