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# a coin is tossed 15 times, then the probability of getting at least 10 consecutive heads, is

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## 15 coins are tossed, then the probability of getting 10 heads will be

A

32768 511 ​

B

32768 1001 ​

C

32768 3003 ​

D

32768 3005 ​ Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is C)

∴ Required probability =

15 C 10 ​ ( 2 1 ​ ) 10 ( 2 1 ​ ) 5 = 15 C 5 ​ 2 15 1 ​ = 5×4×3×2×1 15×14×13×12×11 ​ × 2 15 1 ​ = 32768 3003 ​ Video Explanation

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स्रोत : www.toppr.com

## 1. A coin is tossed 15 times, then find the prob that exactly 9 consecutive heads appears is

1. A coin is tossed 15 times, then find the prob that exactly 9 consecutive heads appears is

Division of Integers

1. A coin is ... Question

1. A coin is tossed 15 times, then find the prob that exactly 9 consecutive heads appears is

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SIMILAR QUESTIONS

Q. A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear isQ. A fair coin is tossed

9

times. Find the probability that it shows head exactly

5 times.

Q. A coin is tossed

m + n times ( m > n )

. (i) Show that the probability of at least m consecutive heads come up is

n + 2 2 m + 1

. (ii) Show that the probability of exactly m consecutive heads come up is

n + 1 2 m + 1 .

Q. Assertion :

A fair coin is tossed

3

times. Consider the events

A

B

C

: exactly two consecutive heads or exactly two consecutive tails.

A , B , C

are independent events. Reason:

A , B , C

are pairwise independent.

Q. A coin is tossed three times, consider the following events:

A : no head appears B :

C :

Which of the following is/are true?

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स्रोत : byjus.com

## A coin is tossed 15 times. What's the probability that exactly 10 heads will occur?

Answer (1 of 5): We will use Binomial Distribution in this case. Since the coin is tossed 15 times. N which is the number of trails will be 15. P = Probability of heads Q = Probability of tails X = No. heads occurring in each toss. So, now we have to find the probability for exactly 10 heads...

A coin is tossed 15 times. What's the probability that exactly 10 heads will occur?

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Sort Sarbari Gupta

Former MSc Big Data Analytics at St. Xavier's College, AhmedabadAuthor has 79 answers and 384.2K answer views4y

We will use Binomial Distribution in this case.

Since the coin is tossed 15 times. N which is the number of trails will be 15.

Q = Probability of tails

X = No. heads occurring in each toss.

So, now we have to find the probability for exactly 10 heads.

P(x = 10) = C(15, 10) P^x Q^N-x

C(15, 10) (1/2)^10 (1/2)^5 = 0.0916

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What are the possible outcomes when a coin is tossed 6 times?

The 64 possible outcomes are listed below.

Now, I can’t help but assume you’re the same anon who asked the same question with 5 coins yesterday. If you ask about 7 coins tomorrow, I will find you. And I will force you to write them out by hand.

HHHHHH HHHHHT HHHHTH HHHHTT HHHTHH HHHTHT HHHTTH HHHTTT HHTHHH HHTHHT HHTHTH HHTHTT HHTTHH HHTTHT HHTTTH HHTTTT HTHHHH HTHHHT HTHHTH HTHHTT HTHTHH HTHTHT HTHTTH HTHTTT HTTHHH HTTHHT HTTHTH HTTHTT HTTTHH HTTTHT HTTTTH HTTTTT THHHHH THHHHT THHHTH THHHTT THHTHH THHTHT THHTTH THHTTT THTHHH THTHHT THTHTH THTHTT THTTHH THTTHT THTTTH THTTTT TTHHHH TTHHHT TTHHTH TTHHTT TTHTHH TTHTHT TTHTTH TTHTTT TTTHHH TTTHHT TTTHTH TTT

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Dewey Abbondanza

B.S. in Industrial Management & Mathematics, Gannon University (Graduated 1972)Author has 2.1K answers and 1.2M answer views4y

The probability of any arrangement of 10 heads and 5 tails is

( 1 2 ) 15 (12)15 and there are 15! 10!5! 15!10!5!

possible arrangements of 10 heads and 5 tails so the answer is

0.091644287 0.091644287 Sergei Michailov

15C10/2^15 = 15C5/2^15 = (15*14*13*12*11)/(5!*2^15)= 0.091644…

Imagine a binary array with 15 places. We need to find out how many ways 10 ones can be placed there. It is 15C10 = 15C5 = (15*14*13*12*11)/5! = 7*13*3*11=3003. (I used identity nCk = nC(n-k) for convenience of calculation). So we have 3003 favorable cases.

The total number of values of that binary array is 2^15=32768.

The result is 3003/32768 = 0.091644…

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A coin is tossed 6 times. What is the probability of exactly 2 heads occurring in the 6 tosses?

Hope a fair coin is tossed.

Each toss has two equally probable options - heads and tails.

Total number of probable outcomes = (2^6) = 64.

Now, total number of outcomes giving exactly two heads = (6C2) * (4C4) = 15 * 1 = 15.

Probability of getting exactly two heads = (15 / 64) = 0.234375.

Total number of outcomes giving at least two heads = total number of outcomes - outcomes giving all six tails - outcomes giving exactly five tails = 64 - (6C6) - (6C5) * (1C1) = 64 - 1 - 6 * 1 = 64 - 1 - 6 = 57.

Probability of getting at least two heads = (57

Anurag Lahon

Love solving and Probability and Statistics ProblemAuthor has 186 answers and 497K answer views4y

Use Binomial Distribution

n=15

probability of head in 1 toss of a coin=1/2

15C10*(1/2)^15=0.09164