When 8 coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads.
Question
When 8 coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads.
Solution
To solve this problem, we need to use the concept of combinations in probability.
-
When no coin turns up as heads: There is only 1 way this can happen, which is when all coins turn up tails.
-
When exactly one coin turns up as heads: This can happen in 8 ways. This is because there are 8 coins, and any one of them can turn up as heads.
-
When exactly two coins turn up as heads: This can happen in "8 choose 2" ways. In mathematics, "n choose r" is a way of selecting r items from a larger set of n items. In this case, "8 choose 2" equals 28.
So, the total number of outcomes in which at most two of the coins will turn up as heads is 1 (no heads) + 8 (one head) + 28 (two heads) = 37.
Similar Questions
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.Outcomes ProbabilityHHT HTH HTT HHH THH TTH THT TTTEvent A: Alternating head and tail (with either coming first) Event B: More heads than tails Event C: A tail on the second toss
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails).The 8 outcomes are listed below. Assume that each outcome has the same probability.Complete the following. Write your answers as fractions.
Two coins are tossed, the probability of getting at least one head isans.
If you flip a coin 8 times, what is the best prediction possible for the number of times it will land on tails?
An eight-sided die is rolled at the same time a coin is flipped. What is the probability of rolling a 5 and flipping a head?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.