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

Question

asked Jul 28, 2020 5.8k views

2 Answers

Vlad Krylov · Answer 1 · 2020-07-29T01:47:36+0000

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

Ninjin · Answer 2 · 2020-07-31T20:28:08+0000

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)!)

_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