Question

An unbiased coin is tossed 15 times. in how many ways can the coin land tails either exactly 5 times or exactly 3 times?

Answer 1

Number of times = 15


`\text {Probability of tails exactly 5 times :}`

`\left(\begin{array}{cc}15\\3\end{array}\right) \bigg( (1)/(2) \bigg)^(15) = (3003)/(32768)`


`\text {Probability of tails exactly 3 times :}`

`\left(\begin{array}{cc}15\\3\end{array}\right) \bigg( (1)/(2) \bigg)^(15) = (455)/(32768)`

Total probability:

`(3003)/(32768) + (455)/(32768) = (1729)/(16384) = 0.11 \text { √(x) (nearest hundred)}`

Answer 2

THis is a binomial distribution:-

P( 3 tails) = 15C3 (0.5)^3(0.5)^12

= 0.0139

P(5 tails) = 15C5 (0.5)^5(0.5)^10

= 0.0916

P(3 or 5) = 0.0139 + 0.0916 = 0.1055 Answer