Question

there are 5 friends in there any two friend birthday in same day than find the probability

Answer 1

Answer:

2.7%

Calculating the probability

n p(n)

5 2.7%

Answer 2

Answer:

The probability of two friends out of five having their birthday on the same day is $0.02$

Explanation:

The probability of an event is calculated using the formula

$P(A)=\frac{n(A)}{n(S)}$

where P(A) is the probability of an event A,

n(A) is the number of favorable outcomes

n(S) is the total number of outcomes.

The concept of combinations will be used to select two friends out of five. In the concept of combinations, the arrangement doesn't matter.

The formula for calculating the number of ways to select r objects from a set of n objects is $^nC_r=\frac{n!}{r!(n-r)!}$

Step-by-step explanation:

Step1-:

For the first person, the probability of having a birthday on any day of the year is $\frac{365}{365}$

Now the second person should have his birthday on the same day so the probability is $\frac{1}{365}$

Now the third person can have his birthday on any of the remaining days except the one selected above so the probability is $\frac{364}{365}$

Now the fourth person can have his birthday on any of the remaining days except the two selected above so the probability is $\frac{363}{365}$

Now the fifth person can have his birthday on any of the remaining days except the three selected above so the probability is $\frac{362}{365}$

Step-2:

Now we have to select any two friends out of five this can be done in $^5C_2$ ways

Step-3:

The probability of two friends out of five having their birthday on the same day is

$P(A)=^5C_2*\frac{365}{365}*\frac{1}{365}*\frac{364}{365}*\frac{363}{365}*\frac{362}{365}=0.02$

Hence, the probability of two friends out of five having their birthday on the same day is $0.02$

What is the probability of an event:

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What is combination, in mathematics:

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