Question

A coin will be tossed 5 times.

The chance of getting exactly 2 heads among 5 tosses is %.

The chance of getting exactly 4 heads among 5 tosses is %.

A coin will now be tossed 10 times.

The chance of getting exactly 2 heads in the first five tosses and exactly 4 heads in the last 5 tosses is BLANK %.

All answers must have three numbers following the decimal.

I just need the answer to the bolded on (where I put "BLANK" just provided the whole question in case it is needed)

Answer 1

p = 0.5

n = 5

This is a binomial distribution

P(X = x) = 5Cx * 0.5^x * (1 - 0.5)^5-x

1) P(X = 2) = 5C2 * 0.5² * 0.5³ = 0.3125 = 31.25%

2) P(X = 4) = 5C4 * 0.5⁴ * 0.5¹ = 0.1563 = 15.63%

3) P(2 heads in first 5 and 4 heads in next 5) = P(X = 2) * P(X = 4)

                                                                        = 0.3125 * 0.1563

                                                                        = 0.0488

                                                                        = 4.88% (ans)