Question

A coin is about to be tossed 50 times. Determine the probability the 8th heads occurs on the 12th toss

Answer 1

The probability of 8th heads,

That is occurred on 12th toss.

Explanation:

A coin is tossed 50 times.

There are two possible outcomes of occurring a head or tail.

Probability of occurring head = no.of head/ possible outcomes

= 1/2

Total number of tossing a coin= 50 times

Probability of 8th heads occurs on 12th toss:

12C8 (1/2)8 (1/2)9 (1/2)10 (1/2)11 (1/2)12

= 12C8 (1/2)8+9+10+11+12

= 12C8 (1/2)50

= 12C8 / 250

= 495 / 1125899906842624

= 4396.48317752 x 10-16

This is the probability of 8th heads,

That is occurred on 12th toss.

Answer 2

0.0806

Explanation:

From the given information:

Number of toss = 50

The probability of having a head = 1/2 = 0.5

The Probability of 8th head occur on 12th toss can be computed as :

Pr(8th head occur on 12th toss) = Pr(7 heads in 11 toss) × P(8th head on 12th toss)

Pr(8th head occur on 12th toss) = C(11,7) × 0.5⁷ × (1 - 0.5)⁴ * 0.5

Pr(8th head occur on 12th toss) =
`(11!)/(7!(11-7)!)` × 0.5⁷ × (1 - 0.5)⁴ × 0.5

Pr(8th head occur on 12th toss) = 0.0806