Four coins fall onto the floor. Find the probability that
(a) exactly three coins land heads up
(b) all coins land tails up
(c) two or more coins land heads up
(d) no more than two coins land tails up
(e) at least one coin lands tails up
How many 5ยข coins make up $2.25 ?
Banagabbababababbabababa
To find the probability of an event, we need to determine the total number of possible outcomes and the number of favorable outcomes. Let's consider each part of the question separately:
(a) To find the probability that exactly three coins land heads up, we need to determine the number of favorable outcomes where three coins land heads up.
There are 4 coins, and each coin can either land heads up (H) or tails up (T). Since we want exactly three coins to land heads up, there are 4 ways this can happen: HHHH, THHH, HTHH, and HHTH.
The total number of possible outcomes is 2^4 = 16 (since each coin has 2 possibilities). Therefore, the probability is 4/16 = 1/4.
(b) To find the probability that all coins land tails up, we need to determine the number of favorable outcomes where all four coins land tails up.
Since there are only two possibilities for each coin (heads or tails), the favorable outcome where all coins land tails up is only one: TTTT.
Therefore, the probability is 1/16.
(c) To find the probability that two or more coins land heads up, we need to count all the favorable outcomes that satisfy this condition.
There are 4 coins and 2 possibilities for each coin. To count the favorable outcomes, we can subtract the number of outcomes where no coins land heads up or only one coin lands heads up from the total number of outcomes.
The number of outcomes where no coins land heads up is 1 (TTTT), and the number of outcomes where only one coin lands heads up is 4 (HTTT, THTT, TTHT, TTTH).
Therefore, the total number of favorable outcomes where two or more coins land heads up is 16 - (1 + 4) = 11. The total number of possible outcomes is still 16. Therefore, the probability is 11/16.
(d) To find the probability that no more than two coins land tails up, we can count the favorable outcomes where either all four coins land heads up or three coins land heads up.
The number of outcomes where all four coins land heads up is 1 (HHHH), and we have already calculated the number of outcomes where three coins land heads up as 4 (THHH, HTHH, HHTH, HHHT).
Therefore, the total number of favorable outcomes is 1 + 4 = 5. The total number of possible outcomes is still 16. Therefore, the probability is 5/16.
(e) To find the probability that at least one coin lands tails up, we can count the favorable outcomes where none of the coins land tails up and subtract it from the total number of outcomes.
The number of outcomes where none of the coins land tails up is 1 (HHHH). Therefore, the total number of favorable outcomes where at least one coin lands tails up is 16 - 1 = 15. The total number of possible outcomes is still 16.
Therefore, the probability is 15/16.
Remember, by understanding the reasoning behind calculating probabilities, you can apply the same principles to solve similar problems in the future.
Each coin can land heads or tails with equal probability of 1/2.
Dropping a coin four times has 2^4=16 possible outcomes.
(a) three heads
By enumeration:
There are four possible outcomes, so the probability is 4/16. THHH,HTHH,HHTH,HHHT.
The number of combinations for 3H can be calculated as 4C3=4!/((1!)(3!))
So probability = 4C3/16
If you are familiar with the binomial probability formula, then
P(3H)=4C3*(1/2)^3(1/2)^1
=4!/(1!3!)*(1/16)=4/16
(b) there can be only one outcome out of 16.
(c)Use enumeration, or combination to find 4C2+4C3+4C4
(d)(e) similar to above.