How many possible outcomes contain at least three heads of the coin is flipped 10 times?

Video Transcript

Hey, it's square. So when you married here, So before I start this, um, start solving this problem. Let's go over the definition of permutation and combination. So permutation is when the order is important. So it's p en coma are which is equal to n factorial over n minus. R. Factorial for a combination. It's when order is not important. So we are seeing an comma are which is equal to the form an arm, which is equal to n factorial over r factorial times and Linus R. Factorial for part A. The coin is flipped 10 times in each footpath, two possible outcomes. So that's just to to the pennant 10th power, just 1024 for part B. We're using combination since the order of heads tails is not important, so n is equal to 10. Are is equal to two. See a 10. Common too, is equal to using the combination formula. Here it's 45 for part C were used in combination again. Since the order is not important this time, we have n is equal to 10 and our is less than or equal to two. So, um where money when we evaluate the definition of a combination. You start with two, start with three and work our way down. Excuse me, this is three and we get 120 and two just 45 one. It just tend zero, which gives us one. We add these all together to get 176 for party. We're using combination again, since the order is not important, so N is equal to turn and there's five for our. Since there's an equal number of heads and tails and 10 flips, so see of 10 Comma five is equal to 252.

University of Pennsylvania

We don’t have your requested question, but here is a suggested video that might help.

Related Question

18. Flip a coin ten times in a row. How many outcomes have 3 heads and 7 tails?

Probability is a part of mathematics that deals with the possibility of happening of events. It is to forecast that what are the possible chances that the events will occur or the event will not occur. The probability as a number lies between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of likely event A is often written as P(A). Here P shows the possibility and A shows the happening of an event. Similarly, the probability of any event is often written as P(). When the end outcome of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occurring.

To understand probability more accurately we take an example as rolling a dice:

The possible outcomes are — 1, 2, 3, 4, 5, and 6.

The probability of getting any of the outcomes is 1/6. As the possibility of happening of an event is an equally likely event so there are same chances of getting any number in this case it is either 1/6 or 50/3%.

Formula of Probability

Probability of an event, P(A) = (Number of ways it can occur) ⁄ (Total number of outcomes)

Types of Events

• Equally Likely Events: After rolling dice, the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 in fair dice rolling.
• Complementary Events: There is a possibility of only two outcomes which is an event will occur or not. Like a person will play or not play, buying a laptop or not buying a laptop, etc. are examples of complementary events.

If a coin is flipped 7 times, then what is the probability of getting 4 heads?

Solution:

Use the binomial distribution directly. Let us assume that the number of heads is represented by x  (where a result of heads is regarded as success) and in this case X = 4

Assuming that the coin is unbiased, you have a probability of success ‘p’(where p is considered as success) is 1/2 and the probability of failure ‘q’ is 1/2(where q is considered as failure). The number of trials is represented by the letter ’n’ and for this question n = 7.

Now just use the probability function for a binomial distribution:

P(X = x) = nCxpxqn-x

Using the information in the problem we get

P(X = 4) = (7C4)(1/2)4(1/2)3

= 35 × 1/16 × 1/8

= 35/128

Hence, the probability of flipping a coin 7 times and getting heads 4 times is 35/128.

Similar Questions

Question 1: What is the probability of flipping a coin 20 times and getting 15 heads?

Answer:

Each coin can either land on heads or on tails, 2 choices.  

(According to the binomial concept)

This gives us a total of 220 possibilities for flipping 20 coins.

Now, how many ways can we get 15 heads? This is 20 choose 15, or (20C15)  

This means our probability is (20C15)/220 = 15504⁄1048576 ≈ .01478

Question 2: What is the probability of 3 heads in 3 coins tossed together.?

Solution:

3 coin tosses. This means,

Total observations = 9(According to binomial concept)  

Required outcome → 3 Heads {H,H,H}

This can occur only ONCE!

Thus, required outcome = 1  

Probability (3 Heads) = (1⁄2)3 = 1/8

What is the probability of 3 heads in 10 tosses?

How many outcomes are there when flipping a coin 10 times?

How many outcomes have at least 3 heads?

How many possible outcomes contain exactly two heads if the coin is flipped 10 times?