Question

A coin is rolled three times.find the probability of getting 2 heads​

Answer 1

There are 8 possible outcomes when you throw a coin three times:

`HHH,\ HHT,\ HTH,\ HTT,\ THH,\ THT,\ TTH,\ TTT`

Out of these combination, the ones with exactly two heads are

`HHT,\ HTH,\ THH`

So, 3 combinations out of 8 have exactly two heads. This means that the probability of having two heads with three coin throws is 3/8

Answer 2

Answer:
`\bold{(3)/(8)}`

Explanation:

Step 1: Numerator

You are looking for an outcome of getting exactly two heads out of a total of three tosses. This can be written as: ₃C₂

The formula for a combination problem is:
`(n!)/(r!(n-r)!)`

• n is the total number of tosses
• r is the total number of successes (in this case, heads)

`_3C_2=(3!)/(2!(3-2)!)=(3*2*1)/(2*1* 1)=3`

There are 3 successes (heads)

Step 2: Denominator

You are looking for the total possible combinations of heads and tails for three tosses (2³)

1st toss and 2nd toss and 3rd toss

2 x 2 x 2 = 8 total possible outcomes