Question

What is the probability of getting exactly two tails when three coins are tossed at the same time?

Answer 1

When three coins are tossed simultaneously, you can use the binomial probability formula to calculate the probability of getting exactly two tails. In this case:

n (number of trials) = 3 (three coin tosses)

k (number of successful outcomes) = 2 (two tails)

p (probability of success on one trial) = 0.5 (since there's a 50% chance of getting tails on one coin toss)

Now, you can calculate the probability:

P(X = 2) = (n choose k) * (p^k) * (q^(n-k))

Where "n choose k" is the binomial coefficient, calculated as C(n, k) = n! / (k!(n-k)!).

P(X = 2) = (3 choose 2) * (0.5^2) * (0.5^(3-2))

P(X = 2) = (3 choose 2) * (0.5^2) * (0.5^1)

P(X = 2) = (3 choose 2) * 0.25 * 0.5

Now, calculate (3 choose 2):

(3 choose 2) = 3! / (2!(3-2)!) = 3

So,

P(X = 2) = 3 * 0.25 * 0.5 = 0.375

So, the probability of getting exactly two tails when three coins are tossed simultaneously is 0.375 or 37.5%.

Answer 2

To find the probability of getting exactly two tails when three coins are tossed at the same time, we need to consider the different ways this outcome can occur.

There are three possible cases in which exactly two tails can occur:

1. Tails-Tails-Heads: In this case, the first two coins should be tails, and the third coin should be heads. The probability of getting tails on a single coin toss is 1/2, and the probability of getting heads is also 1/2. Therefore, the probability of this case is (1/2) * (1/2) * (1/2) = 1/8.

2. Tails-Heads-Tails: In this case, the first and third coins should be tails, and the second coin should be heads. The probability of this case is also 1/8.

3. Heads-Tails-Tails: In this case, the first coin should be heads, and the second and third coins should be tails. The probability of this case is also 1/8.

Since these three cases are mutually exclusive (they cannot occur simultaneously), we can add their probabilities together to find the total probability:

1/8 + 1/8 + 1/8 = 3/8

Therefore, the probability of getting exactly two tails when three coins are tossed at the same time is 3/8.

Answer 3

To calculate the probability of getting exactly two tails when three coins are tossed simultaneously, you can use the binomial probability formula. In this case, you are looking for a combination of two tails (T) and one head (H) in any order.

The probability of getting a tail (T) on a single coin toss is 1/2, and the probability of getting a head (H) is also 1/2.

Now, to find the probability of getting exactly two tails and one head in any order, you can use the binomial coefficient (n choose k), which represents the number of ways to choose k successes out of n trials.

In this case, n (the number of coin tosses) is 3, and k (the number of tails you want) is 2. So, you need to calculate "3 choose 2," which is denoted as C(3, 2). This is calculated as:

C(3, 2) = 3! / [2!(3-2)!] = 3

Now, you need to account for the different ways these two tails and one head can appear in any order, which is 3 ways (TTH, THT, HTT).

So, for each of these 3 possibilities, the probability is:

(1/2) * (1/2) * (1/2) = 1/8

Now, sum up the probabilities for all three possibilities:

(1/8) + (1/8) + (1/8) = 3/8

So, the probability of getting exactly two tails when three coins are tossed at the same time is 3/8, or 37.5%.

Answer 4

The probability of getting exactly two tails when three coins are tossed at the same time is 3/8 or 37.5%.                           

Answer 5

When three coins are tossed simultaneously, there are 2^3 = 8 possible outcomes, as each coin can land heads (H) or tails (T). 

To calculate the probability of getting exactly two tails, you can use the binomial probability formula, where n is the number of trials (3 coin tosses), k is the number of successful outcomes (2 tails), and p is the probability of a single successful outcome (probability of getting a tail on one coin toss, which is 1/2).

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

In this case:

n = 3 (3 coin tosses)

k = 2 (exactly 2 tails)

p = 1/2 (probability of getting a tail on one coin toss)

P(X = 2) = (3 choose 2) * (1/2)^2 * (1 - 1/2)^(3-2)

P(X = 2) = (3 choose 2) * (1/4) * (1/2)

P(X = 2) = 3 * (1/4) * (1/2)

P(X = 2) = 3/8

So, the probability of getting exactly two tails when three coins are tossed at the same time is 3/8 or 37.5%.

Answer 6

When three coins are tossed simultaneously then total outcomes are 

HHH   HTH   HTT  HHT 

TTT    THT   THH  TTH

n(Number of outcomes) is equal to 8

Probability of getting exactly 2 tails are (HTT THT TTH) 3

So, when three coins coins are tossed simultaneously then probability of getting exactly two tails are 3/8

Answer 7

There are three ways this can happen TTH,THT and HTT.The total number of outcomes while tossing a coin is 8 .Therefore the probability is 3/8.

Answer 8

When you toss three coins simultaneously, there are 2^3 = 8 possible outcomes because each coin has two possible outcomes (heads or tails). These 8 outcomes are:

HHH

HHT

HTH

THH

HTT

THT

TTH

TTT

To find the probability of getting exactly two tails, you need to count the number of outcomes that meet this condition. From the list above, there are three outcomes that have exactly two tails: HTT, THT, and TTH.

So, the probability of getting exactly two tails when three coins are tossed at the same time is 3/8, or 37.5%.

Answer 9

I'm happy to assist you with that.

There are eight possible outcomes when three coins are tossed:

HHH HHT THH TTH THT THT HTT TTT

Three heads-up coins are represented as HHH, two heads and one tail by HHT, and so on.

There are three events that can occur if you receive exactly two tails:

HTH HTH THH

The ratio of successful outcomes to total outcomes determines the likelihood of receiving exactly two tails. The chance in this situation is 3/8 since there are 3 successful outcomes and 8 total outcomes.

Alternatively, you might use the probability formula to resolve this issue:

Probability is calculated as (Number of successful outcomes)/(Number of total outcomes).

P(exactly two tails)=(3)/(8)=0.375

I

 hope this is useful.

Answer 10

The probability of getting exactly two tails when coins are tossed at the same time is 3/8

When three coins are tossed simultaneously there are 2^3= 8

Out of these eight outcomes, there are three outcomes that have exactly two tails 

Answer 11

all the outcomes of coins when toosing all three at same time

t=tail of coin

h=head of coiin

ttt

hhh

tth

htt

hth

hht

tht

thh

so here exactly two tt are(tth,ttt,htt)=3/8.