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:  $\bold{\dfrac{3}{8}}$

Step-by-step 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: $\dfrac{n!}{r!(n-r)!}$

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

$_3C_2=\dfrac{3!}{2!(3-2)!}=\dfrac{3\times2\times1}{2\times1\times 1}=3$

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