Question

In rural Ireland, a century ago, the students had to form a line. The student at the front of the line would be asked to spell a word. If he spelled it correctly, he was allowed to sit down. If not, he received a whack on the hand with a switch and was sent to the end of the line. Suppose the student could spell correctly 60% of the words in the lesson. What is the probability that the student would be able to sit down before receiving four whacks in the hand?

Answer 1

The answer is "0.9102"

Explanation:

P(student spell correct) = 0.6

P(student spell incorrect)=1-0.6=0.4

X=the pupil will be allowed to sit down after receiving three slaps on the hand Thus, X would assume Value

X=0 (student sit sans getting whacks)

X=1 (student sit down without receiving 1 whack) (student sit down without receiving 1 whack)

X=2 (student take a seat before receiving 2 whacks)

X=3 (student sit down after receiving 3 punches)

`\to P(X)=0.6 * 0.4^0 +0.6 * 0.4 + 0.6 * 0.4 ^2 + 0.6 * 0.3^3`

`=0.6 * 1+0.24 + 0.6 * 0.09 + 0.6 * 0.027\\\\=0.6 +0.24 + 0.054 + 0.0162\\\\=0.9102\\\\`